MPs will debate holding a second EU referendum after more than four million people signed a petition in protest over the UK's historic ballot on 23 June. The Petitions Committee, chaired by Labour's Helen Jones, scheduled the debate for the afternoon of 5 September.

But Remain supporters should not get their hopes up since the petition was launched before the electorate voted 52% against 48% to break away from Brussels, the debate has no power to change the law and relates to turnout rules.

A House of Commons spokesperson said: "A debate in Westminster Hall does not have the power to change the law, and won't end with the House of Commons deciding whether or not to have a second referendum.

"Moreover, the petition – which was opened on 25 May, well before the referendum – calls for the referendum rules to be changed. It is now too late for the rules to be changed retrospectively. It will be up to the government to decide whether it wants to start the process of agreeing a new law for a second referendum."

The debate will come after the immediate fallout following the Brexit vote, which has included David Cameron's resignation as prime minister, Theresa May's appointment to Number 10, a Labour leadership contest and Nigel Farage's decision to step down as Ukip leader.

Tens of thousands of pro-EU protestors have held demonstrations over the referendum result in a bid to keep the UK in the 28-nation-bloc, but May has promised to eventually trigger Article 50 of the Lisbon Treaty – the mechanism to split from Brussels and start negotiations – and declared "Brexit means Brexit".

However, since the referendum was non-binding some MPs, such as Labour's David Lammy, have vowed to vote down a Brexit if the decision is put to the Commons.

"Parliament now needs to decide whether we should go forward with Brexit, and there should be a vote in Parliament next week," he said in a 25 June statement. "Let us not destroy our economy on the basis of lies and the hubris of Boris Johnson."