David Milliband said the UK should keep the option to back out of Brexit if the final deal is not in the country's best interests.
The former foreign minister said it was right that Parliament would get a vote on the deal - and they should be willing to reject it.
"I think it's imperative that one thing that remains on the agenda is the choice is a choice for Parliament - and if it so desires for the people as well- between life with the European Union and a hard Brexit," he told the Peston on Sunday show.
He also argued that Europe was changing and reforming, with Bo
"I think there is a real momentum now in Europe, an economic mom as well as a political momentum," he said.
"And obviously that mean that the old argument that Europe was this burning house doesn't really stand up."
He suggested that voters had been missold Brexit by claims that the country could pick and mix the best of remaining both in and out of the bloc.
"I think what is becoming clear is that the only form of Brexit that is available is a hard Brexit," he said.
"And of course that is not what was sold, it was the have the cake and eat it that was sold."
"So I think Parliament really has an opportunity to come forward and play its role, because democracy cannot be allowed to die on the referendum day.