The prospect of a parliamentary fightback against the result of the EU referendum gathered pace on Sunday, with pro-remain figures saying they would not “roll over and give up”.

Some are urging a second referendum after Brexit negotiations have taken place.

Lord Heseltine has pointed to the practicalities of an overwhelming majority in the House of Commons against leaving the EU. “There is a majority of something like 350 in the House of Commons broadly in favour of the European relationship,” he said.

“There is no way you are going to get those people to say black is white and change their minds unless a) they know what the deal is and b) it has been supported either by an election or by another referendum,” Heseltine told Sky News. “So there’s a dramatic urgency to get on with the negotiations.”

He called for a cross-party group of MPs to look at the options and “articulate the case for Britain rethinking the result of the referendum”.

Earlier, Tony Blair, the former prime minister, said nothing should be ruled out. “As I’m looking at it here, I can’t see how we can do that. But, you know, the point is, why rule anything out right now?” Blair said the nation needed to consider the consequences of Brexit over the coming weeks and months.

But he added: “I can’t see how you would go through all of the mechanics of another referendum now, I just can’t see it.”

Tim Farron, the Liberal Democrat leader, said his party would not “roll over and give up” over the issue, pledging to fight the next general election on a manifesto promise to take Britain back into the EU. “We are determined to speak to the values that 16 million voted for, and many of the 17 million as well, that Britain is an outward-looking country, not one that isolates itself,” he told the Guardian. “Like all my predecessors I will stand committed to the UK being in the EU.”

Farron said the party recognised the legitimacy of the referendum but would not give up.

Farron’s view is backed up by Labour MP, David Lammy, who said he wanted to meet the Lib Dem leader to discuss the issue. “Economic disaster and the destruction of the union with Scotland loom,” Lammy said. “At the very least we need another vote.”

Writing in the Guardian, Lammy said: “The referendum was advisory and non-binding, in contrast to the referendum on electoral reform in 2011, which imposed a legal obligation on the government to legislate. Almost 500 members of parliament declared themselves in favour of remain, and it is within their powers to stop this madness through a vote in parliament.

“It is also within parliament’s powers to call a second referendum, now that the dust has begun to settle and the reality of a post-Brexit nation is coming into view. We need a second referendum at the very least, on the basis of a plan that is yet to even be drawn up.”