A Labour MP and former minister said the House of Commons should overturn the result of the Brexit referendum.
David Lammy said the parliament should "stop this madness" and "bring this nightmare to an end".
The referendum result is only advisory and is not legally binding in the UK until the Prime Minister triggers the Article 50 clause.
Two thirds of sitting MPs indicated they would vote Remain in the referendum.
Mr Lammy said "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."
UK Labour leader Jeremy Corbyn has already ruled out a second EU referendum despite an online petition calling for a rerun of the vote attracting more than a million supporters.
"The referendum has taken place, a decision has been made, I think we have got to accept that decision and work out our relationship with Europe in the future," Mr Corbyn said.