Nicholson welcomes agreement and urges Europe not to reject new offer
The ball is now in the European Union's court, Ulster Unionist MEP Jim Nicholson said last night.
Reacting to news of the Cabinet talks outcome, he said: "We welcome the fact that the Prime Minister has been able to get a collective Cabinet agreement which reflects what could be a positive deal for the whole of the UK.
"I would urge Mr Barnier and his colleagues not to reject this potential deal. The most important part to note from a Northern Ireland perspective is that this proposal will remove the necessity for the 'backstop' to be implemented.
"The main priority for any unionist and any Prime Minister is that the constitutional integrity of the United Kingdom is protected and not undermined in negotiations."
Mrs May's position could still be under threat from Tory Brexiteers despite the Cabinet agreement.
Pro-EU Tory Dominic Grieve said there had been a recognition that businesses required frictionless trade which meant "we are going to follow EU rules".
He told BBC's Newsnight: "The EU have got to be persuaded that what we are asking them is possible for them within the framework of maintaining their own cohesion, that is clearly going to be a very important discussion."
A 'no deal' Brexit would be "catastrophic for everybody's wellbeing in this country, it would be a great disaster", he said.
Veteran Eurosceptic Sir Bill Cash told Newsnight the plans were "rather disturbing" and he was "deeply disappointed to say the least".
He added: "There are some aspects of it which do fit in to the red lines, but there are many others which raise a lot of very serious questions." Backbencher Andrea Jenkyns said she was "awaiting the detail" of the plans before deciding whether or not to support calls for a leadership contest.
She said the common rulebook would mean "British businesses will continue to be a rule taker from the EU".
Shadow Brexit secretary Sir Keir Starmer said: "It is farcical that it has taken two years for the Cabinet to even attempt to agree a position on the basics of our future relationship with the EU.
"On previous form, whatever has apparently been agreed will struggle to survive contact with Tory MPs and members."
Former Ukip leader Nigel Farage said: "The Tory Eurosceptics are a waste of space.
"No resignations means that the so-called Brexiteers in Cabinet don't have a principle between them, career politicians all."
Business leaders, who have raised concerns about the impact of Brexit on jobs and the economy, also welcomed the Cabinet agreement. CBI director-general Carolyn Fairbairn said it was a "genuine confidence boost" but added: "The hard work starts now, and time is a challenge."