European leaders say they have no "plan B" if the treaty is rejected
Foreign Secretary David Miliband says the UK must ratify the EU Treaty despite its rejection by Irish voters.
The result of the Irish referendum on the Lisbon Treaty should be "respected and digested" but the UK "must keep the ratification process going", he said.
EC President Jose Manuel Barroso said it will be discussed next week but the Tories said it must be "declared dead".
Ireland was the only member state to hold a public vote on the treaty, which must be ratified by all 27 countries.
The British government says the Bill to ratify the treaty will continue its progression through Parliament - despite 53.4% of Irish voters rejecting it in the referendum vote.
Mr Miliband said the Irish result should be respected but there should also be a "British view" on the treaty.
"I think it is right that we follow the view that each country must see the ratification process to a conclusion," he said.
"I believe it is right that we continue with our process and take up the Irish offer of further discussions about the next steps forward."
Mr Barosso called on other members states to continue ratifying the treaty, insisting it was "alive and we should now try to find a solution".
But Conservative leader David Cameron said it would be the "height of arrogance" to continue to try to ratify it in the UK.
"People in Ireland have sent the clearest possible message that they do not want this treaty, they do not want this constitution and by all rights now it should be declared dead."
He said: "I think the elites in Brussels have got to listen to people in Europe who do not want endless powers being passed from nation states to Brussels."
And he added: "It is the height of arrogance for Gordon Brown and our government to press ahead with ratifying this treaty, flying in the face of public opinion."
He said Mr Brown should come to the Commons on Monday to explain what he was going to do and if the treaty was not dead, there should be a referendum on the treaty in the UK.
Under Irish law, any amendment to an EU treaty requires an amendment to the Irish constitution and all constitutional amendments require approval by referendum.
The treaty is designed to help the EU cope with its expansion into eastern Europe and was due to come into force on 1 January 2009.
It provides for a streamlining of the European Commission, the removal of the national veto in more policy areas, a new president of the European Council and a strengthened foreign affairs post.
Former Europe Minister Denis MacShane conceded that the Lisbon Treaty "may well be dead" following the Irish vote.
But the Labour MP added: "I personally think that a vote in a foreign country should not determine the democratic decisions taken in the British Parliament."
UK Independence Party leader Nigel Farage, who campaigns for Britain's exit from the EU, said the treaty had been "kicked it into the long grass".
And he reacted angrily to Mr Barroso's suggestion it was not dead, saying: "This reaction shows more than even the gaping chasm that exists between the people and the politicians. What part of 'no' don't they understand?"
But Ed Davey, Lib Dem international affairs spokesman, said it was a "disappointing" result because it was a "good treaty for Ireland and good for Europe".
The House of Lords is due to have the third reading of the Bill on 18 June.