UK officials have attacked the tactics of France and Germany in the run-up to a deal on the European constitution and presidency.
President Chirac wants no more "dilutions" of the EU constitution
The prime minister's official spokesman warned against leaders "playing games" at the EU summit in Brussels.
Criticism of the UK's position by the French president was "unfortunate", said the spokesman.
But after two days of intensive talks, diplomats say a deal has now been done over the EU's first ever constitution.
BBC political correspondent Guto Harri said a British source had told him a deal had essentially been agreed.
EU leaders have now reconvened to make their comments the final text of the constitution before making a formal announcement. But there have been several delays already on Friday evening.
Meanwhile, Ireland's Europe Minister, Dick Roche, has said efforts to secure a deal over who will succeed Romano Prodi as the European Commission president could be postponed until a later date.
Earlier, France and Germany told the summit that they would accept a compromise on the constitution put forward by Ireland but go no further.
The UK's prime minister's spokesman had earlier reflected British irritation at France and Germany.
"What we all now have to accept is we are operating in a Europe of 25, not a Europe of six or two or one," said the spokesman.
"Let's not do this in a spirit of playing games, let's do it in a spirit of general consensus."
French President Jacques Chirac, who on Thursday accused Tony Blair of trying to water down the constitution, indicated he was worried by the direction the summit was taking and would accept no further retreat.
British officials say they are unhappy that German Chancellor Gerhard Schroeder has tried to link the EU presidency with any trade-offs over changes to the constitution.
And Mr Straw told the BBC: "I am worried, of course, because it would be far better if there could or could have been a consensus in respect of the presidency of the commission.
"I'm also concerned that this is not a particularly edifying spectacle all the way across Europe."
The foreign secretary said splits between European leaders proved that the EU remained a "union of proud, independent nation states" rather than a superstate.
Mr Straw seemed to rule out the chances of Belgian Prime Minister Guy Verhofstadt succeeding outgoing EC President Romano Prodi.
The foreign secretary said he liked the candidacy of former senior Conservative Chris Patten "a great deal". France is opposed to the idea and favours Mr Verhofstadt.
It is thought Irish premier, Bertie Ahern, might volunteer to do the job himself as a compromise.
Mr Straw said the constitution was needed to make the EU more "efficient and effective" now it was a union of 25, not 15, members.
Rejecting claims that British ministers were posturing at the talks, he added: "This constitution will be good for Britain provided our concerns are met."
Ministers have promised a referendum on any treaty and have vowed to protect British vetoes on issues like defence, foreign policy and taxation.
But the Conservatives continue to urge Mr Blair to veto the whole constitution.
Tory leader Michael Howard branded as "nonsense" talk of Mr Blair taking a tough stance.
He told reporters: "I think this is all a put-up job. The truth is that Tony Blair's 'red lines' are red herrings.
"This constitution gives masses of more power to Brussels from Britain."
Asked about the possibility of his former cabinet colleague Mr Patten becoming EU president, Mr Howard said none of the candidates shared his own view of the need for a more flexible Europe.
But Mr Patten did understand the importance of keeping EU regulations to a minimum, he added.
Mr Blair has said Britain should stay at the centre of European decision-making and not become marginalised despite the UK Independence Party raising its share of the vote at last week's European elections.
Liberal Democrat leader Charles Kennedy said voters would be distrustful of leaders arguing about commission jobs instead of focusing on the big question of restructuring the enlarged EU.
The new president should be chosen not through "nationalistic horse trading" but on their competency, he argued.