Voters are strongly opposed to either Tony Blair or David Miliband taking up top Brussels jobs to be created under the Lisbon Treaty, according to a poll.
While the former prime minister's prospects of becoming president of the European Union are slipping, Mr Miliband is being hotly tipped to become its first foreign minister.
But an ICM poll for The Sunday Telegraph revealed widespread hostility among the British public towards either Mr Blair or the Foreign Secretary getting the positions.
Some 53% of voters did not want Mr Blair to become EU president, while 36% did. A YouGov poll earlier this week put opposition at just 31%.
Opposition to Mr Miliband becoming the EU's high representative was put at 48%, while support for him stood at just 29%.
He has repeatedly insisted he is not in the running for the position, but European leaders have been increasingly talking up his suitability for it.
ICM also found that the Tories were currently commanding a 17-point lead over Labour in the polls. Support for the Tories stood at 42%, compared with 25% for Labour. The Liberal Democrats were on 21%.
Nick Griffin has failed to improve the British National Party's electoral prospects with his recent Question Time appearance.
Support for the far-right party was on 2% - one point down on a its score in a similar poll conducted by ICM in the days leading up to last week's high-profile show on BBC1. However, 15% of voters were found to agree with the BNP's hard-line stance on immigration of introducing a total ban.
Some 66% said there were too many immigrants in the UK.
