The frontrunner for the EU's top job has told the Guardian that David Cameron will have to yield to the rest of Europe's choice on his selection – even though no one in Britain will have voted in the European parliamentary election for the bloc he leads.

Under a new system, the leading bloc in the election will be able to propose a candidate to head the European commission. Because Cameron withdrew from the centre-right European People's Party in 2009, no British votes will go to the frontrunning EPP and its leader, Jean-Claude Juncker.

Juncker, the former Luxembourg prime minister, said it was not his problem that Europe might end up with a commission chief for whom no one in Britain had voted.

"Cameron has to stick to the clear treaty rules," Juncker told the Guardian and four other European newspapers. "The treaty is the treaty. And whoever wins, wins."

Juncker is fighting Martin Schulz, a German social democrat and the president of the European parliament, to replace José Manuel Barroso as head of the European commission. Current opinion polls have the centre-right slightly ahead of the social democrat bloc in the European parliament elections, making Juncker the leading challenger for the commission post.

This is the first time this has happened. Commission chiefs have always been appointed as a result of a stitch-up between EU national leaders. In what is claimed to be a more democratic process, the blocs of parties in the elections have selected their own contenders for the commission job.

"The question is not whether we are supported in Great Britain," Juncker said in a campaign debate between the two frontrunners staged by the Guardian and its European newspaper partners. "The question is rather why does Great Britain not stick to the vote of the continental Europeans? There are another 27 countries who will have voted this way."

But senior officials and diplomats in Brussels say Cameron is not the only national leader who is deeply unhappy with the new "democratic" approach. Some see it as a power-grab by the European parliament in determining who should lead the commission.

"It completely changes the way the EU is governed, the way the commission works," said a senior diplomat. "You can't vote for the EPP in Britain. It's preposterous, ludicrous."

Immediately after the elections at the end of the month, national EU leaders are to dine in Brussels to thrash out who should take over at the commission. Under the Lisbon treaty, their nomination has to take account of the election results and be supported by an absolute majority in the parliament.

It is possible that neither of the two frontrunners will ultimately get the job, though that would risk accusations of a democratic fiasco.

Leaving Britain out of his argument, Schulz said: "If these 27 [government heads] say after the elections that they're not taking either of us, that would really be a deviation from democracy and would do great damage."

Ed Miliband, the Labour leader, has declined to support Schulz, and Labour has told him not to campaign for his Party of European Socialists (PES) in Britain. Schulz is currently crisscrossing the continent and last week visited Northern Ireland but stayed away from the rest of the UK.

While Juncker emphasised that it was not his problem that Britons could not vote for him, he has also highlighted negotiations with Cameron aimed at keeping Britain in the EU as a central part of his pitch for the commission job.

But he added that an "accommodation" with Britain should not entail reopening the EU treaties, as pushed by Cameron.

He said he had received no overtures from the British government, but added: "We can't escape this debate with the UK. It will be wise to start with this issue."

While accepting that he was out of the running for votes in Britain, Juncker stressed that his rival, Schulz, was also not supported there.

The difference is that the Labour party belongs to the PES bloc and that votes cast for Labour in the UK automatically help Schulz's cause.

"The British campaign is a special election campaign for all of us," said Schulz. "But Great Britain is only one country of 28. Convincing [Cameron] to support me would be rather difficult. He will have an important say, but certainly not the final say."