Ex-European Commissioner Neil Kinnock says the treaty on the EU constitution is dead after the French voted "No".
Kinnock: Referendum results have to be listened to
But the former Labour leader said the UK government could not be seen to say that ahead of the Dutch vote on 1 June and its pending presidency of the EU.
Lord Kinnock warned that it would be "a mistake" for EU leaders to set aside any votes that reject the constitution.
He said the constitution was overly complicated and the EU needed to "strip it to essentials".
Almost 55% of French people voted "No" and 45% "Yes", in the country's vote on Sunday.
The Dutch are also predicted to return a similar result when a referendum is held in Holland on Wednesday.
Tony Blair said it was too early to say whether Britain will hold a referendum on the constitution - a vote that was expected next spring.
1 June - Dutch referendum on the constitution
6 June - Jack Straw makes Commons statement
16 June - Meeting of European leaders
1 July - UK takes over EU presidency
He called for "time for reflection", saying France's rejection of the document raised profound questions about Europe's future.
Foreign Secretary Jack Straw is to make a statement to MPs in the Commons on Monday on the implication of the French vote.
There had been a suggestion that he would use it to announce whether the government would continue with its plans for a referendum on the constitution.
However, the Prime Minister's official spokesman said: "I would see Monday's statement as more of an update."
Ex foreign secretary Robin Cook said sorting out the crisis would give Mr Blair "the best possible curtain call for himself to make a graceful exit".
Lord Kinnock said there was "no doubt at all" that the treaty was now dead, following the French vote.
"I realise why our government cannot say that - there's a referendum tomorrow in the Netherlands and the UK government is about to assume the six monthly presidency of the European Council," he told BBC Radio 4's Today programme.
"Referendums produce results and results have got to be lived with.
"The leadership of Europe has now got to do what it should have done for years past ... go for a propaganda-free, explicit, factual strategy of tireless explanation.
He said he had been "utterly disgusted" with elements of the French left which had joined "fundamentally reactionary and disgusting elements" of the political scene in the "no" campaign.
Lord Kinnock argued that the UK was in a good position to lead the EU out of its present crisis by using its six-month presidency, which begins on 1 July, to implement measures to modernise the economy.
He said the UK was not alone in wanting to vastly improve productivity, skills and competitiveness, he insisted.
Former Conservative prime minister John Major said there was no point in the UK holding a referendum if the treaty was dead.
He said it was in the UK's economic interests to "resurrect the affection" for Europe that was once there
The constitution's stated aim is to streamline decision-making in the enlarged EU of 25 countries. It has to be ratified by all member states to become law.