Lord Hattersley, who was forced to pull out of the event due to illness, told BBC Radio 4’s Today programme that leaving the EU would be much worse than remaining.
The 86-year-old, who was a minister in the Wilson and Callaghan governments, said: “I think the British people have a right to cast a vote on the merits of the package Mrs May has negotiated.
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“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.”
The Sheffield rally was one of 170 People’s Vote events held around the country three days before the crucial vote on Theresa May’s deal in the House of Commons.
Lord Hattersley was due to speak alongside Labour former cabinet minister Dame Margaret Beckett and Liberal Democrat leader Sir Vince Cable.
He was expected to say there is “no conceivable deal which is remotely as beneficial to Great Britain as full membership of the European Union”.
Tory former minister Anna Soubry and Labour MP for Wakefield Mary Creagh also spoke at the event as part of the People’s Vote campaign’s national “Day of Action”.
Lucy Holland, from student campaign group For Our Future’s Sake, told the audience of around 500 people that young people would not forgive and forget over Brexit.
She said: “If you take away our future it is going to affect yours, because it is hard to be Prime Minister if young people don’t vote for you.
“The path forward now is clear, there is only one way to fix this mess. That’s a people’s vote on the Brexit deal.”
The audience sent their best wishes to Lord Hattersley with a round of applause.
Additional reporting by PA
The Independent has launched its #FinalSay campaign to demand that voters are given a voice on the final Brexit deal.