David Cameron is to demand that fellow EU leaders explain their decision to back Jean-Claude Juncker as the next European Commission president this week after they appeared to give up on finding an alternative.

Downing Street made clear last night that the prime minister, angry at attempts to push a decision through in the face of UK opposition, will force an unprecedented vote at an EU summit on Friday and ask heads of government to explain why they are not willing to consider other names.

Herman van Rompuy, president of the European council, who was charged with banging heads together to find an alternative to the former Luxembourg prime minister, will meet Cameron and Nick Clegg in London on Monday. But EU officials say the talks will be more about how to salvage some form of agreement about other EU positions – including portfolios for UK and other commissioners – and a form of wording about the EU's priorities under the new commission, than a chance to discuss rival candidates to succeed outgoing commission president José Manuel Barroso.

Cameron's failure – which he hopes to turn into a heroic lone stand against his EU counterparts – to block Juncker comes as an Opinium/Observer poll finds far more people saying they would vote to leave the EU under current rules than to stay in.

Cameron has promised an in/out referendum by the end of 2017 and has said he will campaign for a Yes vote having renegotiated substantially different and improved terms of British membership.

Some 48% of voters said they would currently vote to leave the EU in a referendum, while 37% would vote to stay.

However, if Cameron were able to secure a deal which he said had redefined the terms of membership, this would change, with 42% in against 36% who would vote to leave.

But – with a defeat over Juncker likely to increase scepticism – only 18% of voters (including 34% of Conservatives) think Cameron is likely to be able to achieve satisfactory terms of renegotiation while 55% say this is unlikely.

Early on Friday senior UK government insiders were likening Cameron's chances of blocking Juncker's candidacy to England's then slim chances of staying in the World Cup following two defeats to Italy and Uruguay.

While there is little enthusiasm for Juncker in other member states, Angela Merkel now wants the matter settled this week – as does Matteo Renzi, the prime minister of Italy, which will hold the EU presidency from 1 July. Merkel was furious with Cameron for saying that Juncker's appointment would push the UK closer to the EU exit door.

Germany's chancellor is also under pressure from her own Christian Democrat party, as well as their Social Democrat coalition partners, to back Juncker, while Renzi does not want the issue to remain unsettled when his country takes the EU reins.

With France and Spain also unwilling to oppose Juncker, preferring to focus on commission portfolios for their nominees, and the Swedes and Dutch unwilling to oppose Germany's will, Cameron's long and determined search for allies appears to have been fruitless. One EU source aware of Van Rompuy's position said: "It is clear that there will not be a blocking minority and that will be that."

, which will begin with a dinner in the Belgian town of Ypres on Thursday, to commemorate the centenary of the first world war.In the past, the choice of commission president has been decided by consensus among EU heads of state and government without the need for a vote, but Cameron wants to place his opposition to Juncker on record when the summit moves to Brussels on Friday.

He is understood to be ready to tell other leaders that in 2004 the UK did not push for Chris Patten to be president of the commission because of French opposition, and that he wants explanations about why the same consideration from other EU leaders is not being shown to the UK.

Tory MPs are ready to back Cameron's lone fight, even if he is isolated in defeat, with many seeing Juncker's appointment as strengthening the case for the UK to get out of a union of which it is an increasingly uncomfortable member.

German opposition to Cameron's anti-Juncker drive intensified further after Tory MEPs joined forces with the small German Eurosceptic party AfD in the European parliament. Shadow Europe minister Gareth Thomas said Cameron was allowing his party to drift to the extremes of the political debate in Europe. "The AfD are Merkel's electoral opponents, and the decision has proved an unnecessary and unhelpful strain on a key alliance at a crucial time. What started as a political management problem for Cameron risks turning into a crisis between Britain and one of our most crucial European allies, and now it is Britain's influence and standing in Europe that is at risk of being undermined as a result."