The Conservatives have challenged Foreign Secretary David Miliband to a televised debate on the EU treaty.
Mr Hague called for a 'proper public debate' on the treaty
Shadow foreign secretary William Hague said Labour had broken its "solemn manifesto promise" to hold a referendum out of "sheer arrogance".
Earlier, Mr Miliband dismissed calls for a public debate on the treaty - which replaces the defunct EU constitution - as "navel-gazing".
But veteran Labour politician Tony Benn said change was being "imposed".
The government has repeatedly rejected calls for a referendum on the treaty, saying it is not as significant a change as the ill-fated EU Constitution, on which a vote was promised in Labour's 2005 manifesto.
The treaty has been brought in to replace the planned constitution, which was killed off after referendums on it were lost in France and the Netherlands.
The Conservatives want a referendum to be held on the treaty, saying that it is much the same as the constitution.
The treaty proposes having a president of the European Council for two-and-a-half years, replacing the current system where countries take turns at being president for six months.
It also calls for a single foreign affairs supremo, a smaller European Commission and the removal of national vetoes by member states in a number of areas.
Mr Hague said a referendum was a matter of "trust and accountability".
He added: "Labour, like every other political party, gave a solemn manifesto promise that the EU constitution would be for the British people to decide in a referendum. But Gordon Brown now says he sees no need to keep that promise.
"And the substance of the new treaty would mean that, over time, there would be a decisive shift of power from Britain to the EU.
"People would find that more and more decisions on foreign policy and criminal justice would be made not by British MPs answerable to them at the ballot box, but in Brussels."
Mr Hague said it was "vital that there is a proper public debate so that the British people are fully involved in a question vital to our country's future".
He added: "It should not be confined to Parliament or party conferences.
"To dismiss public concern at a breach of manifesto promise on a treaty that almost every EU leader has said is the EU Constitution by another name is sheer arrogance."
But Mr Miliband, speaking at Labour's annual conference in Bournemouth, said: "Europe needs to look out, not in, to the problems beyond its borders that define insecurity within our borders.
"It doesn't need institutional navel-gazing and that is why the reform treaty abandons fundamental constitutional reform and offers clear protections for national sovereignty.
"It should be studied and passed by Parliament." On the Conservatives, he added: "Europe has divided them for 15 years and it's not going to divide us."
On Monday Mr Benn told a Labour conference fringe meeting he thought Prime Minister Gordon Brown would eventually give in to pressure for a referendum.
Liberal Democrat leader Sir Menzies Campbell said last week that the public should get a vote on whether to stay in the EU, arguing that this would mean a more "honest debate" on the UK's position.