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."

The government's response to the petition

The European Union Referendum Act received Royal Assent in December 2015, receiving overwhelming support from Parliament. The Act did not set a threshold for the result or for minimum turnout.

The EU Referendum Act received Royal Assent in December 2015. The Act was scrutinised and debated in Parliament during its passage and agreed by both the House of Commons and the House of Lords.

The Act set out the terms under which the referendum would take place, including provisions for setting the date, franchise and the question that would appear on the ballot paper. The Act did not set a threshold for the result or for minimum turnout.

As the Prime Minister made clear in his statement to the House of Commons on 27 June, the referendum was one of the biggest democratic exercises in British history with over 33 million people having their say.

The Prime Minister and Government have been clear that this was a once in a generation vote and, as the Prime Minister has said, the decision must be respected. We must now prepare for the process to exit the EU and the Government is committed to ensuring the best possible outcome for the British people in the negotiations.