Former Labour deputy leader Roy Hattersley has said he supports another Brexit referendum "very strongly".
The politician said Britons have "a right" to have their say on Theresa May's Brexit deal, which goes to a vote in the Commons on Tuesday.
A People's Vote event has been held in Sheffield, with Dame Margaret Beckett and Sir Vince Cable speaking.
Lord Hattersley said those who voted to leave the EU had "no idea" what that would mean.
Former Irish Prime Minister John Bruton has also said that the UK's approach to Brexit meant it had decided to "tear up" the Good Friday Agreement.
Lord Hattersley, 86, who was due to speak at the rally but pulled out due to illness, told BBC Radio 4's Today programme: "I think the British people have a right to cast a vote on the merits of the package Mrs May has negotiated.
"They voted by a small majority to leave the union, but they had no idea what leaving the union meant.
"We now know how bad it will be. We now know that it will be much worse than remaining in, and that the British people have a right to express a view on whether they want to remain in or they want to leave."
He added that "sometimes, you just have to do what is right", rather than looking at what "wins elections" and possibly at the risk of losing Labour supporters.
No deal would be the worst possible scenario and needed to be avoided, said Lord Hattersley, who previously said that leaving the European Union would be a "disaster".
The peer, a minister in the Wilson and Callaghan governments, added that he did not think a general election - which Labour leader Jeremy Corbyn has called for - would happen.
MPs are widely expected to reject Mrs May's deal on Tuesday, negotiated between the EU and UK, with more than 100 Conservative MPs among those expected to vote against it.
Transport Secretary Chris Grayling earlier told the Daily Mail that not leaving the EU would cause the 17 million people who voted for Brexit to feel "cheated". He said blocking Brexit could lead to a surge in far-right extremism.
Lord Hattersley dismissed those comments, saying not many would regard Mr Grayling as "an expert in these matters".
Pro-EU former Conservative minister Anna Soubry also criticised Mr Grayling's comments as "irresponsible nonsense".
David Lammy, a Labour former minister, said it was "a desperate attempt by a government minister to use a tiny far-right minority to hold our democracy to ransom", adding: "It is gutter politics."
Ms Soubry was also among those at the Sheffield rally. Lord Hattersley had been due to say that the "vast majority" of Labour members want the party to campaign for a new Brexit referendum if hopes of an early general election are extinguished.
He was to say that "no conceivable deal which is remotely as beneficial to Great Britain as full membership of the European Union" and that young people would pay the price for Brexit.
Meanwhile, hundreds of people have been attending an anti-austerity march in central London.
The event was organised by The People's Assembly Against Austerity, with speakers including shadow chancellor John McDonnell.
People gathered outside the BBC's New Broadcasting House before marching to Trafalgar Square, many wearing yellow vests - which national organiser Ramona McCartney said was to show "solidarity with the left and working class in France".
France has seen weeks of anti-austerity demonstrations by those wearing the vests, known as the "gilets jaunes" movement.
Addressing protesters in Trafalgar Square, Labour's John McDonnell said eight years of austerity was "tearing apart the very social fabric" of the UK.
He said when "the time is right", his party will move a motion of no confidence in the government. He read a message from Mr Corbyn, saying a general election was needed to bring about a "fairer, more equal society".
An anti-austerity protest also took place in Belfast city centre.
Separately, there was a march in central London which was broadly pro-Brexit, BBC home affairs correspondent Daniel Sandford said, but smaller than the anti-austerity rally, with between 200 and 300 attending.