Former Tory Party chairman Chris Patten has announced he will not now stand for the presidency of the EU's executive Commission.
A replacement must be named within the next month
Mr Patten, currently the EU external affairs commissioner, was reported to be Downing Street's choice.
Germany and France's preferred candidate, Belgian Prime Minister Guy Verhofstadt, has also stepped down.
European leaders have yet to resolve their dispute over potential candidates.
Britain and other member states objected to Mr Verhofstadt's federalist vision of EU integration.
But neither Mr Patten nor Mr Verhofstadt are understood to have had sufficiently broad support.
On Friday member states finally agreed an EU constitution that will ease the bureaucratic pressures of enlargement.
The unresolved issue of finding a successor for current European Commission president Romano Prodi will be dealt with in later talks.
French President Jacques Chirac said the decision had been postponed "for
a few days".
European commissioner and former Labour leader Neil Kinnock welcomed the
He said he would like to see the job given to the Portuguese commissioner for justice and home affairs Antonio Vitorino.
Mr Kinnock said he was a multilingual moderniser and manager with huge experience and intelligence.
Romano Prodi leaves the job in October, but his replacement must be named
within the next month.