The Tories have challenged Gordon Brown to "trust the people" by holding a referendum on a new EU treaty.
Mr Hague said the referendum is an issue of trust
Shadow foreign secretary William Hague says the treaty, published in draft form on Monday, would "fundamentally change" Britain's place in the EU.
In a speech he said Labour had promised a referendum on a constitution and said trust in politics was at stake.
The government says a referendum is unnecessary as the treaty is not a constitution, but is good for Britain.
The treaty, expected to be finalised later this year, preserves much of the planned EU constitution rejected by Dutch and French voters in 2005.
But the constitution's envisaged post of "foreign minister" has been changed in favour of a "high representative" for foreign policy and a reform of the EU's voting system was delayed until at least 2014, to placate Poland.
In a speech to the Policy Exchange, Mr Hague said there was "near unanimity" across Europe that the treaty was "simply the substance of the EU Constitution repackaged".
"With power transferred from Britain to Brussels in spades and the EU fundamentally changed there is no question but that the constitution by another name merits a referendum," he said.
He said the referendum issue went "to the heart of the issue of trust in politics" and said there would be little time for Parliament and the public to discuss the treaty before a deal was done.
"Only by a referendum can the British people hold anyone to account over this treaty," he said.
There will be three months of talks on the text of the new treaty aimed at reforming the 27-member European Union. The final text is expected to be ready in time for a summit in Lisbon in October.
Foreign Secretary David Miliband said on Monday the concept of a constitution had been "abandoned" and the government did not see the need for a referendum.
He added: "I think it is a good treaty for Europe and for Britain because it takes forward institutional reform in a sensible way and undermines the arguments of those saying that there is a superstate around the corner.
"It is evident that that is not the case."
But UK Independence Party leader Nigel Farage told the BBC "there is little doubt it's the old EU constitution that has come forward".
Europe Minister Jim Murphy told BBC Radio 4's Today programme: "We wouldn't sign up to any treaty that transferred in any significant way, any UK sovereignty to the European Union."
When it was put to him that others said there had only been cosmetic changes to the old constitution, he said: "The UK has signed up to a UK version of the European treaty. We've got a series of opt-outs - on justice and home affairs for example."