The Prime Minister was also warned of a new Conservative revolt following the dramatic Commons vote in which Tory rebels joined forces with Labour MPs to defeat the Government and demand a real-terms cut in the EU’s budget for 2014-2020.
Mr Cameron and Mr Clegg stood shoulder to shoulder on that occasion, arguing that a freeze in Brussels’ spending was the most the Government could realistically expect from the negotiations.
But the Liberal Democrat leader spelt out the differences between the Coalition partners at a speech in London.
Mr Cameron has signalled his desire to repatriate some powers from Europe – for example over employment laws – during negotiations on a fresh EU treaty.
But his Liberal Democrat deputy said: “I want to focus on the proposal doing the rounds that the best way to improve the UK’s position in Europe is to renegotiate the terms of our relationship with the rest of the EU. We should opt out of the bad bits, stay opted in to the good bits, and the way to do that is a repatriation of British powers.
“That seems very reasonable. In fact, it’s a pretty seductive offer – who would disagree with that? But look a little closer, because a grand, unilateral repatriation of powers might sound appealing but in reality, it is a false promise, wrapped in a Union Jack.”
Mr Cameron’s spokesman responded: “I don’t think it’s news to anyone that the Prime Minister and the Deputy Prime Minister, the Conservatives and the Liberal Democrat party, have slightly different positions on Europe.”
William Hague, the Foreign Secretary, has launched a full-scale review of how EU legislation affects Britain which is expected to form the basis of proposals to retrieve powers from Brussels.
The Prime Minister is unlikely to get the opportunity to repatriate powers before 2015, but the issue is likely to be key division between the parties at the next general election.
But Mr Clegg’s intervention means clear that he would block any attempt by the Tory leader to repatriate powers while the Coalition is still in power.
The Liberal Democrat leader also signalled he was heading for conflict with the Prime Minister over moves to opt out of some 130 EU law-and-order measures and then adopt a smaller number.
Mr Clegg said he would be guided by the police and the security services on whether to retain measures such as the European arrest warrant, which are opposed by many Tories.
Meanwhile ministers today made clear they would not be bound by the result of Wednesday’s vote in negotiations over the EU budget.
The Chancellor, George Osborne, refused to promise his party’s Eurosceptics to lobby for a real terms cut. He said: “We will veto any deal that is not good for the British taxpayer. We will only put to the House of Commons a deal that is good for the British taxpayer. That is our position. It is the beginning of a negotiation. Let’s see where that negotiation leads.”
Downing Street also played down the likelihood of the Prime Minister achieving a reduction in EU spending, saying the fact that recipient nations also held a veto put the UK in a “very challenging position”.
But Mark Pritchard, one of the leading Tory rebels, said: “If the Government ignores the voice of the people through their elected representatives in Parliament, it will confirm that Britain is effectively run by an elected dictatorship.”
Douglas Alexander, the shadow Foreign Secretary, said: “Nick Clegg’s words say more about his frustrations about the chaos in the coalition than anything else.
“Labour have argued consistently for a real terms cut in EU spending because we don’t believe Europe could or should be exempt from the challenge of doing better, with less.”
Q&A: European Union budget
How big is the European Union budget?
It will be about €147bn (£118bn) in 2012, a rise of 3.5 per cent on last year.
The money comes mainly from contributions from member states, as well as a proportion of VAT levied by each country and duties on imports from outside the EU.
Where does it go?
About 94 per cent – €138.9bn (£111.4bn) – is redistributed around the EU.
This year some €58.2bn (£46.6bn) will be spent on the cohesion and structural funds which pump cash into the EU’s less prosperous areas.
A further €58.6bn (£47.1bn) is spent on the Commons Agricultural Policy either through direct payments to farmers or the rural development fund.
The other six per cent – €8.3bn (£6.7bn) – is spent on administration.
What is it likely to rise to?
The European Commission has proposed raising the budget by five per cent to €987.6bn (£793.3bn) to cover the years 2014-2020. This works out at an average annual budget of €164.6bn (£132.2).
David Cameron argues that it should only increase by the rate of inflation (currently around two per cent). Britain has not specified a figure, but it could be in the region of €900bn (£723bn).
The EU’s 27 members have a variety of positions – although it is clear Britain is among the most hawkish.
How much does the UK contribute?
Britain last year handed over some €12.1bn (£9.7bn), direct to the EU (excluding VAT receipts), but received back some €6.7bn (£5.4bn), over half of which went on farming subsidies. Britain is one of nine EU members that are net contributors to its overall spending.
Why do other countries benefit more than Britain?
It’s largely a matter of prosperity, with member states more likely to be net recipients of EU cash the further to the east and south they are.
The three biggest financial gainers from the EU are Poland, Spain and Greece.