David Cameron has begun a week of intense political infighting over Europe by becoming embroiled in a furious row with Nicolas Sarkozy over Britain's role in talks to solve the crisis enveloping the euro.

The bust-up between Cameron and Sarkozy held up the conclusion of the EU-27 summit for almost two hours, with the French president expressing rage at the constant criticism and lectures from UK ministers.

Sarkozy bluntly told Cameron: "You have lost a good opportunity to shut up." He added: "We are sick of you criticising us and telling us what to do. You say you hate the euro and now you want to interfere in our meetings."

The prime minister has torn up his travel plans this week – a move urged on him by Labour leader Ed Miliband in a Guardian interview on Saturday – to attend an emergency heads of state meeting on Wednesday, and has demanded that all 27 EU countries be given the final say over measures to prevent the eurozone's sovereign debt crisis spreading and Europe sliding into deep recession.

On Monday the prime minister is facing both the largest Commons revolt of his premiership and the largest rebellion of eurosceptics suffered by a Conservative prime minister when parliament votes on whether the UK should have a referendum on Europe.

Cameron will meet parliamentary aides in Downing Street before the vote in an attempt to dissuade as many as 10 members of the government minded to rebel against the prime minister, requiring them to resign their posts. The government is sticking to its decision to impose a three-line whip on MPs to vote against the motion despite criticism it has been too heavy-handed.

Officials who witnessed the angry exchanges between Cameron and Sarkozy said the prime minister insisted that the package to be adopted on Wednesday by the 17 eurozone countries had serious implications for non-euro countries in the EU and their interests must be safeguarded. Eventually, after what Donald Tusk, the Polish prime minister, who chaired the summit, called a "stormy" discussion, the French president secured an agreement that all 27 leaders will first debate the three-pronged package of measures to recapitalise banks, build up the bailout find and write down Greek debt, but then the eurosummit would have the final say at back-to-back summits on Wednesday.

Cameron, however, got his fellow leaders to insert into the final communique recognition that laws on the single market must be upheld and a level playing field safeguarded for countries not in the euro. He later brushed aside the divisions, saying that what mattered was that markets regain confidence that the eurozone is preventing contagion from the Greek debt crisis.

The vote in parliament on Monday will be a testy encounter with his own party on Britain's membership of the EU. The vote calls for a nationwide referendum on whether Britain should leave the EU, renegotiate its treaty with Brussels, or remain a member on current terms. The government will not suffer a defeat, since Labour and the Lib Dems will vote down the motion, but a voluble and sizeable group believe the prime minister should honour pledges once made to allow a national poll on Britain's relationship with Europe. They would like the repatriation of social and employment rights.

On Sunday in Brussels, Cameron used a press conference to appeal directly to potential rebels, talking up the chance of repatriating powers with the "possibility" of treaty change coming on to the agenda as early as December, as euro countries push towards fiscal integration.

He claimed he had proved his ability last year to "exact" a good price when he agreed an EU treaty change that created a new mechanism for bailing out troubled eurozone countries but exempted Britain from having to pay for bailouts from 2013.

It is not clear if this would trigger the government's stated commitment to a referendum because it is due to stage a vote only if new powers are transferred from Westminster to Brussels, and any change by Cameron would be likely to do the reverse.

"If there is a treaty change, that gives Britain an opportunity," Cameron said. "Treaty change can only happen if it is agreed by all the 27 member states of the European Union.

"Any treaty change – as the last treaty change did – is an opportunity for Britain to advance our national interest. The last limited treaty change which brought about the European stability mechanism gave us the opportunity to get out of the euro bailout fund that the last government opted into."

Cameron said: "I've also argued that this crisis means that greater fiscal and economic integration of the eurozone is inevitable. But this must not be at the expense of Britain's national interest. So I've secured a commitment today, which will be in the council's conclusions, that we must safeguard the interests of countries that want to stay outside of the euro, particularly with respect to the integrity of the single market for all 27 countries of the EU.

Academics at Nottingham University predict the number rebelling against the government is likely to top the 41 Conservative MPs who voted against John Major in May 1993 on the third reading of the Maastricht bill – the biggest backbench rebellion for a Tory PM on Europe on whipped business.

They also said 41 was the number who rebelled in October last year over an attempt to make using insulting language a criminal act, which was then the biggest rebellion of Cameron's premiership.

The two sides in the referendum battle fortified their positions, with government ministers defending the decision to impose a three-line whip on the vote brought to the Commons by a petition.

The defence secretary, Philip Hammond, said the whip had been put in place because the motion was contrary to government policy and holding a referendum on the EU would be "just a distraction".

The former Conservative leader Lord Howard also weighed in, saying that an EU referendum would be a mistake in current conditions. The former foreign secretary Sir Malcolm Rifkind said he believed a vote for a referendum would make Britain a "laughing stock".

But Cameron faces the likely resignations of some parliamentary aides to ministers and rebellion by the chairman of the 1922 committee, Graham Brady. Lord Tebbit suggested that "not even Ted Heath faced the chairman of the 1922 voting against him".

The number rebelling could hit 90 if the 68 who signed up to the original amendment tabled by the MP for Bury North, David Nuttall combine with another 33 who have signed compromise amendments which ministers say also run counter to government policy. Nuttall would commit the government to holding a referendum by May 2013 but would give the public three options – keeping the status quo, leaving the EU or reforming the terms of the UK's membership.

An amendment from George Eustice, a new but influential MP who used to work for Cameron, calls on the coalition to publish a white paper in the next two years setting out which powers ministers would repatriate from Brussels. The government would then renegotiate the UK's relationship with the EU and hold a referendum on the outcome.

Some names on Eustice's list may have signed up in the brief window when they thought Eustice's amendment would come to be adopted by the government as a way of the party high command giving backbenchers a compromise to vote through.The Commons speaker John Bercow may however choose not to call Eustice's amendment.