Theresa May is threatening to turn the UK into an offshore "bargain basement" economy, Labour leader Jeremy Corbyn has warned as he demanded more details on the Prime Minister's Brexit strategy.
Mr Corbyn expressed concern at the tone of Mrs May's keynote address on how she plans to handle looming "divorce" negotiations with Brussels.
The Labour leader said: "Throughout the speech there seemed to be an implied threat that somewhere along the line, if all her optimism of a deal with the European Union didn't work, we would move into a low-tax, corporate taxation, bargain basement economy on the offshores of Europe.
"I think she needs to be a bit clearer about what the long-term objectives are."
Liberal Democrat leader Tim Farron accused Mrs May of a "theft of democracy".
"Theresa May has confirmed Britain is heading for a hard Brexit. She claimed people voted to leave the single market. They didn't. She has made the choice to do massive damage to the British economy.
"Theresa May also made clear that she will deny the people a vote on the final deal. So instead of a democratic decision by the people in the country, she wants a stitch-up by politicians in Westminster.
"The people voted for departure, they should be given a vote on the destination. This is a theft of democracy.
"This speech was a mixture of vague fantasies and toothless threats to our nearest neighbours. At the moment Britain needs friends more than ever, she has succeeded in uniting the rest of Europe against her.
"When it comes to British prosperity and British democracy, she is waiving the white flag from the White Cliffs of Dover."
Unite general secretary Len McCluskey said the PM was trying to "appease the hard right" in her party and Ukip by talking tough on immigration, as he warned the Government stance puts jobs at risk.
"Trade unions and others have clearly outlined how real concerns over the freedom of movement can be addressed by sensible labour market safeguards without abandoning the single market when we leave the EU.
"Out of the single market, possibly out of the customs union, then investment in core sectors like car manufacturing, chemicals, aerospace, even food manufacturing, will be threatened as companies face hefty on-costs and serious disruption to their supply chains.
"The Prime Minister must pay less heed to the Brexit headbangers around the Cabinet table and more to the anxiety felt by working people who believe their jobs are being held hostage by the extreme nationalist wing of her Government."
TUC general secretary Frances O'Grady said: "Signs that the UK will leave the single market are reducing confidence in the British economy and the falling pound looks likely to keep pushing up prices on everyday goods this year.
"The Prime Minister's plan for Brexit ... must make sure that wages keep rising, as well as protecting jobs and rights, so that working people don't pay the price for the decision to leave the EU."
Adam Marshall, director general of the British Chambers of Commerce, said: "While businesses now have a clearer sense of the Prime Minister's top-line priorities, they will come away from her speech knowing little more about the likely outcome of the Brexit negotiations than they did yesterday.
"The simple fact is that businesses all across the UK are carrying on. Directly affected companies are being pragmatic, and are preparing for a range of possible outcomes."
Paul Everitt, chief executive of aerospace and defence trade body ADS, said: " The Prime Minister has provided important clarity ahead of the triggering of Article 50 and the start of formal Brexit negotiations.
"Securing the best deal for the UK and our EU partners will take time and it is essential that there are transitional arrangements in place to avoid disrupting closely integrated supply chains and damaging the UK's global competitiveness."
Allie Renison of the Institute of Directors said: "We welcome the level of detail provided in the PM's speech and her commitment to providing certainty wherever possible, which is absolutely vital for business if they are to navigate and make the best of Brexit.
"While we do not expect a running commentary, firms hope to get periodic updates to maintain confidence as we make our way towards the exit.
"We now know that we will be leaving the single market, and while there will be firms who regret this, they will at least be able to plan on that basis."
Greenpeace UK's head of public affairs Rosie Rogers said: "Whatever position people take on Brexit, it's a fact that leaving the single market would undermine vital environmental and consumer protections we now take for granted.
"Many of the laws that keep our bathing water clean and control dangerous air pollution and toxic chemicals come from the EU.
"Without EU laws and courts to underpin and enforce them, they could be left at the mercy of ministers who may ignore them and scrap them with a stroke of the pen."
Shadow Brexit secretary Sir Keir Starmer said Mrs May's position meant she had ruled out a "hard Brexit" with no agreement and World Trade Organisation rules governing future dealings with the EU.
He told BBC Radio 4's World At One the vote promised to Parliament meant "she has to keep to the ambitions she has set out".
Lloyd's of London boss Dame Inga Beale said the insurance giant would continue with its plan to open a subsidiary office within the EU's single market.
She told the programme: "What we need is the licensing and the regulatory ability to be able to provide insurance to the EU customers that we have. Without access to the single market we are not going to be able to continue to do that for some of our business from London as we have done, traditionally, for many years."
Dame Inga said the subsidiary office would be able to handle the 5% of the business that came from EU policyholders.
"While we have got some more certainty about where the Government is heading on this, for us it doesn't make a difference, we are still going to go ahead with our plans to open a subsidiary."
German MEP Elmar Brok, a member of Angela Merkel's CDU party, said the trade deal would not be possible within the two-year Article 50 timetable.
A trade deal could take "four or five years" so "we will need a transitional period between Brexit and the clarification of the new relationship", he told World At One.
Home Secretary Amber Rudd, a prominent campaigner on the Remain side in the referendum, said a work permit regime was an option for the new immigration system which will follow Brexit.
"The only thing I can say with absolute certainty on immigration with the EU is it will no longer be freedom of movement - that was the one area the Prime Minister was absolutely crystal clear on," she told the programme.
A work permit system was "one of the ways we are looking at, but it's not the only way".
Speaking from the European Parliament in Strasbourg, Ukip leader Paul Nuttall said he would give Mrs May "seven out of 10" for her speech.
"Some of it did sound like a Ukip conference speech and she's now applying some of the things that we've been talking about for many, many years," he said.
"I am concerned that what we're getting is some sort of slow-motion Brexit where she is speaking about interim measures, or a transitional period, which will only begin after April 2019.
"She has given no end date to these transitional measures. I challenge the Prime Minister; let's have this all done and clean before the next general election in 2020."
The general secretary of the GMB union, Tim Roache, said: "Fantastical speeches and wishful thinking is all well and good, but what does this actually mean for British jobs and industry in the coming years?
"A leap in the dark and political platitudes just won't cut it for families trying to budget and plan for the future. When it comes to the day-to-day impact of the Government's Brexit policy on working people, sadly it's still as clear as mud."
Unison general secretary Dave Prentis said: "People know we're leaving Europe, but are worried about what Brexit means.
"The Prime Minister says she wants to reassure people working in our public services and she will protect employment rights that started out in Europe. But without the detail many will sleep uneasy."
Labour MP Chuka Umunna, of the Vote Leave Watch campaign, said: "If Brexit means anything, it means continuing to trade on current terms with the EU, and doing nothing that will cost jobs and growth - for that is what Leave campaigners promised.
"Now the Prime Minister is giving up single market membership before negotiations have even begun, and has not ruled out the nightmare scenario of no deal being done, which would mean Britain falling on to WTO (World Trade Organisation) rules in our trade with the EU.
"This would increase tariffs, cut jobs, and lead to higher inflation."
The chief executive of the Chartered Institute of Public Finance and Accountancy, Rob Whiteman, warned that Mrs May had provided "little certainty" for public services, which rely on a healthy economy and access to labour and expertise.
"The EU will be playing hardball, so we cannot assume it will agree to a bespoke arrangement that would serve UK interests," said Mr Whiteman.
"This is a game of Russian roulette, where the prize is not committing economic suicide."
Mark Porter, British Medical Association council chairman, said: "At a time when the NHS is struggling to cope with mounting pressures and significant staff shortages, the Prime Minister must deliver on her promise to guarantee the rights of EU nationals in Britain, and Britons living in Europe, as soon as possible.
"There are more than 10,000 doctors from the European Economic Area working in the NHS, so it is vital for the stability of the NHS and the future of medical research that the Government removes the ongoing uncertainty and grants them permanent residence.
"The immigration system must remain flexible enough to recruit doctors from overseas, especially where the UK workforce is unable to fill vacant roles."
Antony Walker, deputy chief executive of techUK, said: " The risk of falling off a regulatory cliff edge in two years' time has not gone away. However if a smooth and orderly exit can be achieved from the EU then the UK's thriving tech sector can go on to be the powerhouse of global Britain."
British Retail Consortium chief executive Helen Dickinson said: "The Prime Minister has an ambitious plan with the right priorities. It is crucial that Britain gets a new deal that works for ordinary British consumers, which doesn't hit them with the costs of new import tariffs at a time when the pound is already weakened.
"The Government has an opportunity to secure a win-win deal that works for the UK economy, by keeping prices down for consumers, while allowing the EU to continue benefiting from its open-trade relationship with the UK."
Green Party co-leader Caroline Lucas said: "Theresa May has confirmed today that she is willing to take an extreme gamble with our country's future. Her plan for Britain to be out of the single market and out of the customs union, without any guarantees on the kind of bilateral trade deals we'll have, is extremely risky.
"The Prime Minister has morphed a close-run referendum into a mandate for an extremely hard Brexit which will see our economy harmed as part of her desperate desire to end free movement."
CBI director-general Carolyn Fairbairn said: "Today the Prime Minister changed the landscape.
"Ruling out membership of the single market has reduced options for maintaining a barrier-free trading relationship between the UK and the EU. But businesses will welcome the greater clarity and the ambition to create a more prosperous, open and global Britain, with the freest possible trade between the UK and the EU.
"The pressure is now on to deliver these objectives and achieve a smooth and orderly exit.
"Businesses want to make a success of Brexit but will be concerned about falling back on damaging WTO (World Trade Organisation) rules. They stand ready to support the negotiations to get the best possible deal for the UK by ensuring that the economic case is heard loud and clear."
Former chancellor Lord Lamont told the Press Association: "The Prime Minister has given a firm lead and a clear vision. She has given all the detail that could reasonably be expected.
"Carping or calling for yet more detail will merely undermine Britain's negotiating position. It is time for everyone to back the Prime Minister's efforts."
Federation of Small Businesses national chairman Mike Cherry said the group's members wanted to see the "bold and ambitious" free trade deal promised by the Prime Minister and the group would " push the Government to guarantee whatever transition process is put in place ensures there is no cliff edge or gap in trade".
He added that exports could be boosted if small firms were offered the right support from Government along with the promised free trade agreements (FTAs) around the world.
"Global trade will only flourish if the FTAs prevent additional barriers, such as cost and paperwork," he said.
Roland Rudd, chairman of Open Britain, which has campaigned for the UK to remain part of the single market, said: "The Government must now explain how they can deliver on the trade, free of tariffs and bureaucratic impediments they have promised. As the Chancellor has said, no one voted to be poorer and it would be an act of calamitous self-harm if any second-best trade arrangement with the EU damaged British growth, jobs and prosperity.
"By threatening to walk away without a deal, the Prime Minister has raised the very real prospect of us defaulting on to WTO rules and erecting punishing tariffs and regulatory barriers between ourselves and our largest trading partner.
"It is now more vital than ever that those of us opposed to a hard and destructive Brexit continue to make our voices heard as we embark on a set of negotiations which will shape our country for decades to come."
Dave Smith, chairman of the Institution of Engineering and Technology's innovation panel, said: "While it gives greater clarity about the kind of Brexit we can expect and when it will happen, today's speech leaves a number of unanswered questions for the UK's engineering and technology sectors, particularly around how the Government intends to maintain ideas and innovation sharing between the UK and the rest of Europe - something which is greatly enabled today by movement of people here from outside the United Kingdom.
"In particular, we urge the Government to provide further clarity on how the UK will be able to recruit the estimated 182,000 new engineers needed over the next decade - as well as how it intends to ensure our standard of research in technology and innovation will remain competitive after the UK's likely forced withdrawal from European research programmes."
Foreign Secretary Boris Johnson said Mrs May's "powerful" speech will be "well received" by EU nations.
Speaking to reporters at Lancaster House, he went on: "Because it's negotiable, this is something that I think will be good for the UK and good for the rest of the EU as well."
Asked why the EU would give the UK a "free lunch", Mr Johnson said: "As the Prime Minister said, I think it's going to be good for both sides."
He went on: "We very strongly think this is in our mutual interest, we're not leaving Europe, we're disentangling ourselves from the treaties of the EU, we can remain powerfully committed to Europe with a new European partnership... whilst also going forward with an identity as global Britain."
The Brussels official leading Brexit negotiations said the EU was "ready as soon as (the) UK is" to start the process, but talks could only begin once Article 50 had been triggered.
The European Commission's Michel Barnier said on Twitter: "Agreement on orderly exit is prerequisite for future partnership. My priority is to get the right deal for EU27."
Arron Banks, the Leave.EU campaign founder, said: " Theresa May made big promises today, but so did her predecessor. Cameron went to Brussels acting tough, but he crumbled at the first sign of resistance and came back with nothing.
"With the promise of a parliamentary vote on her deal with the EU, May has opened the door to a Remainer coup. The House of Lords is a chamber of party political cronies, unfit for purpose. If she delivers on Brexit as she promises, it will be a miracle. Until then we won't be letting our guard down."
Vote Leave's former chief executive Matthew Elliott, now the editor-at-large of the BrexitCentral website, said: " She painted an inspiring vision of a global Britain with which only the most recalcitrant Remain supporter could disagree.
"I hope that those who have been thus far reluctant to accept the referendum result will now get behind this optimistic vision as the Prime Minister prepares to go in to bat for Britain."
The National Farmers Union said it was seeking urgent talks with Government over its "legitimate and important concerns" following the PM's speech.
In a statement, the NFU Council said: "The Prime Minister has ruled out the UK's continuing participation in the European single market or the EU customs union and instead has stated her intention to pursue a free trade agreement with the EU.
"We hope the Prime Minister's ambition can be achieved, but as we know these kind of deals normally take years to conclude and do not cover all products. If a quick and comprehensive deal cannot be achieved, it would be absolutely vital that there are appropriate phased arrangements to avoid a disruptive cliff-edge to allow Britain's farmers to adapt."