David Lammy, MP for Tottenham and a former minister under Tony Blair and Gordon Brown, said the UK needed to "wake up" and wants parliament to stage a vote next week so it can overrule the electorate's decision to Leave the EU.
In a statement issued this afternoon, Lammy, who ran against Sadiq Khan to be Labour's candidate for London mayor, said: "We do not have to do this. We can stop this madness and bring this nightmare to an end through a vote in parliament.
"The referendum was an advisory, non-binding referendum. The Leave campaign's platform has already unravelled and some people wish they hadn't voted to Leave. Parliament now needs to decide whether we should go forward with Brexit, and there should be a vote in Parliament next week."
He added: "Let us not destroy our economy on the basis of lies and the hubris of Boris Johnson."
|Brexit Britain: What you need to know|
Reports of disgruntled Leave campaigners who would like to now change their mind circulated over the weekend, though the only evidence presented of disappointment was anecdotal. More than 17.4m million people - 51.9 per cent - voted to leave the EU in Thursday's vote which was one of the largest democratic exercises in the UK's history.
A petition launched before the referendum seeking to change the rules so a vote to Leave or Remain would require more than 60 per cent on a turnout of more than 75 per cent had gained 1.7 million signatures by Saturday afternoon - the most ever for a campaign of its type.
However, it was widely dismissed as a pointless stunt, and the fallout from Thursday's historic vote continued to cause ripples.
The UK's top representative in Brussels, European commissioner Lord Hill, also stepped down after campaigning for the UK to Remain. David Cameron suggested the UK could be without representation in the EU's executive arm after his departure as he confirmed the decision over Hill's replacement would be one for his successor - who will not be in place until October.