The UK will face a "lesser future" if it leaves the European Union, Sir John Major warned as he urged leaders on the continent to accept changes are needed to ease the pressures caused by the number of migrants coming to Britain.
The former prime minister, who has warned the UK's membership of the EU is in the balance, urged other European states to agree to measures to help curb the number of migrants from within the union.
He said the issue is not a "uniquely British problem", and he is confident a solution could be found despite leaders including German Chancellor Angela Merkel ruling out changes to the principle of free movement within the EU.
Sir John, who addressed members of the German chancellor's party in Berlin last week, said there had been a "huge bulge" in numbers coming to the UK, but the problem "may only be relatively short-term".
Warning of the consequences of a British exit from the EU, Sir John said: "Of course there would be a future. But it would be a lesser future."
He added: "I really would not want to be the prime minister who had to explain that we are sinking to a much lower level of relevance in the world outside the EU, with the doors in the corridors of power being closed to us.
"On every count, despite its frustrations - of which there are many, despite the reforms we need - which are many, we are far better off in the European Union than outside it and, most important of all, we are far better off for the next generation and the generation after that if we are in."
Sir John said the UK's word would mean less and its economic power would be "materially decreased" outside the EU.
"Britain has been a great nation in the last 300 years. Do we really want to sink to a lower level of relevance outside the European Union?"
David Cameron has promised to put immigration at the heart of his plan to renegotiate the UK's relationship with Brussels before an in/out referendum by the end of 2017 if he remains in Number 10.
Sir John told BBC1's Andrew Marr Show: " We aren't seeking to end free movement, but what has been happening over the last few years has been such a huge bulge in the amount of migrants coming to the UK - our population has risen by about 7% in a decade and at the present rate the British population would rise in a few decades by 25% while the German population would have fallen.
"I think as people begin to see the particular circumstances that we face I think there will be a good deal of sympathy for the difficulty, and the European Union has a good deal of finding a way around difficult corners like this."
The former premier insisted he is not anti-immigration, saying "we wouldn't have a National Health Service without migrants, we would not have a transport system without migrants", but the problem is "purely numbers, and it may only be relatively short-term".
He added: "I see it as a shortish-term problem, maybe not a year, maybe longer, and we need a little help over that period."
Sir John said he believes a way can be found to make changes without altering the fundamental principle of free movement.
"I think there are some practical things that could be done that don't infringe the principle but do meet the problem," he said.
The former Tory chief said Mrs Merkel is not the only leader opposed to changes in free movement rules, but there are other countries who share the UK's concerns.
"It's not just Angela Merkel, of course she is hugely important... but it is an agreement we have to have across the European Union.
"It's not only we who face trouble. Many of the far-right parties, many of the anti-social parties who offer nothing but negativity across Europe - in Greece, in Sweden, in many countries including our own - have an antipathy to immigration because immigration is seen by their populations at too high a level, as causing difficulties.
"It's not just a uniquely British problem. It's uniquely difficult for us, because of the numbers and because we, for example, are a fraction of the landspace of France or Germany."
Following his recent return to the political fray on the issue, Sir John was as ked if he would be prepared to help lead the negotiations.
"I think not, I think it will have to be someone who is in the Government and is close to the Prime Minister in the Government, but a great deal of the most important negotiations... will inevitably be done by the Prime Minister himself."
He disagreed with Foreign Secretary Philip Hammond's assessment that the UK has to be prepared to walk away from the table if a deal cannot be reached.
"I don't think it's a question of saying we would walk away if we fail because I don't anticipate failure," he said.
Sir John's intervention came as the Government faced questions about its handling of European Union budget negotiations amid allegations that Chancellor George Osborne struck a secret deal over the UK's contributions to Brussels.
Despite previously opposing proposals to boost the EU's contingency fund for this year, Britain abstained in a vote that would have handed an extra £2.4 billion to the European Commission, the Sunday Times reported.
The move led to claims - strenuously denied by the Treasury - that the UK agreed not to oppose the move as part of the effort to reduce the surprise £1.7 billion surcharge demanded from the UK by Brussels last month.
Following talks between the EU finance ministers on Friday, Treasury Financial Secretary David Gauke abstained even though other countries opposed to higher spending - including Germany, France, Netherlands, Sweden, Denmark, Austria and Finland - voted against the plans, the newspaper reported.
The proposals were rejected but the commission intends to return with new ones, and if passed British taxpayers would be liable for a £400 million share of the £2.4 billion.
The Sunday Times said one foreign diplomat claimed the abstention could have been linked to the deal struck on the £1.7 billion demand, which has been reduced to £850 million as a result of the UK's rebate, payable in instalments next year rather than by the original December 1 deadline.
"The only rationale is that they are giving full priority to the membership fee and they have put down all their other objections and struck a deal with regard to that," the diplomat said.
The Treasury insisted there had been no deal with the commission, and the decision to abstain was simply because the extra £2.4 billion was a "reprofiling" of the existing budget.
A spokesman said: "The Government is approaching discussions on the EU budget in the same way it always does - getting the best deal for British taxpayers.
"Thanks to the deal secured by the Prime Minister last year, the size of the EU budget will fall this year compared to last year."
But shadow chancellor Ed Balls said: "George Osborne needs to come clean about his secret deal in Brussels over the EU budget."
Work and Pensions Secretary Iain Duncan Smith said he is optimistic European leaders will find a solution on freedom of movement within the EU, noting privately he had heard officials from across the continent recognise there is an issue.
On the need for more control over freedom of movement within the European Union, Mr Duncan Smith said most people would agree with Sir John.
He described recent research, which suggested European migrants made a £20 billion contribution to the UK between 2001 and 2011, as a "silly report".
Mr Duncan Smith told BBC Radio 5 Live's Pienaar's Politics: "First of all, you've got to take them all the way through until they get older and they actually start taking from the state.
"You don't account for the fact often in many communities they literally change the schooling because so many people arrive not speaking English, you've then got problems about local services, transport, all that kind of stuff.
"So the reality is that what (Sir John) is saying is right - Europe as a whole needs to tackle this because when the GDP of the various economies were about the same, the freedom of movement was really a fairly balanced process but once you get economies that are not the same, so you get big difficulties and (Sir John) is simply warning what the Germans already know privately and have said to me they need to sort this problem out."
Told publicly there appeared no visible willingness from other European countries to give on the principle of free movement within the EU, Mr Duncan Smith said Prime Minister David Cameron would lay out more clearly in the coming weeks his position.
Asked if other leaders would give ground on the issue when it came to it, he replied: "All I know is that in my discussions with senior MPs, members of the Bunderstag and also others around Europe - and I've travelled most of the countries in Europe, certainly the bigger countries including Italy, Spain, Netherlands and Denmark and various other countries, talked to them all including Germany - and once behind closed doors their general sense is 'look, there is an issue here'.
"The issue is the numbers coming in causing distortion problems and therefore they have to deal with it.
"The only question is what agreement do they come to.
"I'm, as ever, much more positive. People used to say the same about (Margaret Thatcher) and the rebate. Everyone said 'there will be no rebate, Britain will never get a rebate' - low and behold after negotiations we got it."
He went on: "My general view is I think people know and they value the UK's involvement and they will want to find some kind of solution.
"It's not only for the UK, Spain has a very similar problem where they have a very high number of eastern Europeans entering their country at a time of very high domestic unemployment. This puts huge strains on them."
Asked if he believed a Tory-led exit from the EU is more likely than not, Mr Duncan Smith said: "No I don't... I actually think all these organisations are meant to be shaped around the greater good and we have profoundly believed for some time that the nation state must drive much more of what happens in Europe, that we are together with Europe for co-operation and trade where it suits and benefits us across the board, but not for that kind of level of intrusive involvement that means governments cannot govern themselves."
Shadow foreign secretary Douglas Alexander said: "I think it's a tragedy for Britain that we are seeing more effective leadership from an ex-Conservative prime minister than the present Conservative Prime Minister."
He told Sky News: "Of course there is reform and change that can be secured within Europe in relation to immigration and in relation to other issues. I thought John Major made a convincing case that change is possible.
"The tragedy for the UK is that we have a Prime Minister today who is so weak in the face of his own backbenchers internally, and the threat of Ukip externally, that he seems incapable of grasping that reform opportunity."
Mr Alexander acknowledged that the "scale of immigration we have seen in recent years has brought to bear particular pressures on particular communities, that's why we need to see sensible reforms".
A British exit from the European Union would be a "disaster", Italy's prime minister said.
Matteo Renzi said if the British voted to sever ties with Brussels, it would be damaging for both the UK and the EU.
Speaking at the G20 summit in Brisbane, he said: "I think this could be a disaster. A disaster for Europe, obviously, I believe also for the UK. This is my opinion.
"We need a UK able to invest in a different idea of Europe - more supportive in relation with citizens and not with the power of bureaucrats," he told Sky News.
"For this reason Europe needs the role of the UK, but I believe also at this moment the UK has a lot of advantage in the presence in Europe."
Tory chairman Grant Shapps said freedom of movement could not be an "open-ended deal" and the UK should have "some control" over the number of migrants coming in.
He acknowledged the Tories had "a problem" with hitting their target of reducing net migration to the tens of thousands by the end of the parliament, partly because of EU migrants attracted by the relative strength of the British economy.
"From outside Europe we have been very successful, from inside Europe we have a problem, which has been spurred by the fact that we've had the fastest growing of the economies in Europe and that's attracting people here and we don't think we've had sufficient controls over that."
Mr Shapps told Sky News: "David Cameron, absolutely rightly, is saying on behalf of the British people we don't think this is an open-ended deal, we believe that we should have some control over people coming here.
"People can come here to work, yes, but not to claim benefits."
He added: "Most people in this country think Europe is too big, too bossy, too interfering."