Prime Minister Gordon Brown is eroding trust in the political system by rejecting calls for a referendum on the EU treaty, according to William Hague.
Critics say the treaty is the constitution by another name
The shadow foreign secretary says Mr Brown's decision not to hold a poll is a "nakedly cynical" calculation that he can "bulldoze" the treaty into law.
Tory leader David Cameron is emailing party supporters urging them to back the cross-party referendum campaign.
The government insists a referendum is not necessary.
In a speech to the Centre for Policy Studies in London, Mr Hague said since becoming prime minister Mr Brown had made it clear he wanted to revive trust in the political process and to involve people in the development of policy.
But he stressed that following his refusal to call a referendum, "in future no-one can have any sensible grounds for believing a political promise from Gordon Brown".
"It is bizarre that Gordon Brown should try to begin his premiership by embarking on a course for which he has no democratic mandate, in total breach of an absolutely clear-cut manifesto commitment and wholly undermines the rhetoric with which he is trying to surround his government.
"The calculation he has made is nakedly cynical: that it would cause him too much political trouble to keep his promise and hold a referendum when he could give the EU Constitution a few tweaks, rename it and bulldoze it through without anyone noticing or minding too much.
"I suspect he may now be having his doubts about whether he got that judgment right."
Mr Hague said the treaty negotiated in Brussels in June was "the constitution by another name" and therefore Mr Brown should honour Labour's manifesto commitment on a poll.
He insisted that the demand for a referendum did not represent a lurch to the Right in his party.
An "overwhelming majority" of British voters - more than 80% in one poll - backed a referendum, which was also supported by the TUC and a growing number of Labour MPs, he said.
"The present government's attitude that Europe is too complicated a subject to be left to he voters, so that manifesto promises about the EU can consequently be dropped, is actively working to erode trust in our political system."
He added: "This is not an issue that is going to go away, nor should it.
"As Northern Rock has lately shown in a textbook example, every system of human interaction is ultimately based on trust.
"If that trust goes, the system will break down. The way Gordon Brown has disregarded his promise of a referendum is a dangerous thing for politics as a whole."
In his email to thousands of Tory activists, Mr Cameron called for them to sign an online petition started by the I Want A Referendum campaign to make sure "Gordon Brown keeps his promise".
"Better still, send this email to five people you know and ask your friends and colleagues to sign up," he said.
Mr Brown says a referendum is not necessary because the new EU treaty is not the same as the constitution - on which the Labour government promised a poll, until it was rejected by Dutch and French voters in 2005.