The Government has rejected a call for a second referendum on European Union membership in a petition that was signed by more than 4.1 million people following the Brexit vote.

It was the most-signed Government petition since the process was introduced in 2011.

However in an official reply, the Foreign Office said 33 million people had had their say and “the decision must be respected”.

“We must now prepare for the process to exit the EU,” it said.

The petition, which was set up by a Brexit supporter before the referendum was held, had called for the Government to annul the results if the Remain or Leave vote won by less than 60 per cent on a turnout of less than 75 per cent.

Government petitions which reach over 100,000 signatures must be considered for debate in parliament.

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The Foreign Office said: “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.”

In the wake of the Brexit vote, the petition was shared widely on social media by Remain supporters.

As the number of signatories soared, the petition's original author, Leave activist William Oliver Healey, disowned it, saying his opinions on the need for a high turnout and high level of support for one side had been “hijacked” by EU supporters.

The Government’s decision will come as a blow to those who hoped to find a parliamentary means of stopping Britain’s withdrawal from the bloc.

However, calls for a second referendum on the terms of Britain’s departure from the EU are gathering pace. Four out of 10 people would like to see a second referendum before Britain leaves the EU, according to an opinion poll for The Independent.

The survey of 2,000 people by ORB found that 40 per cent agree that there should be a referendum on the exit deal that the Government negotiates, and that the UK should seek to Remain in the EU if the public rejects the terms.

Brexit protest: Thousands march in London Show all 12 1 /12 Brexit protest: Thousands march in London Brexit protest: Thousands march in London A woman poses with a home-made European Union flag as Remain supporters gather on Park Lane in London to show their support for the EU in the wake of Brexit PA Brexit protest: Thousands march in London Remain supporters demonstrate in Parliament Square PA Brexit protest: Thousands march in London Tens of thousands of people gathered to protest the result of the EU referendum PA Brexit protest: Thousands march in London A majority of people in the capital voted to remain in the European Union Reuters Brexit protest: Thousands march in London Protesters chanted: “What do we want to do? Stay in the EU” PA Brexit protest: Thousands march in London The march follows a similar rally in Trafalgar Square that was cancelled due to heavy rain – but which tens of thousands of people turned up to anyway Reuters Brexit protest: Thousands march in London Britain voted to leave the European Union in a referendum by 52 per cent to 48 per cent Reuters Brexit protest: Thousands march in London But support for the Leave campaign in urban areas and among young people was significantly lower Rex features Brexit protest: Thousands march in London Marchers gathered at Park Lane at 11am and marched towards Parliament Square PA Brexit protest: Thousands march in London Some protesters held up baguettes in a display of affection for our continental neighbours PA Brexit protest: Thousands march in London The disparity between different parts of the country has promoted a four million signature petition calling for a second referendum and even a renewed push for Scotland to cede from the UK PA Brexit protest: Thousands march in London The event’s organiser, King’s College graduate Kieran MacDermott, wrote: “We can prevent Brexit by refusing to accept the referendum as the final say and take our finger off the self-destruct button" Reuters

Such a course was supported by 12 per cent of people who voted Leave last month. A second vote was backed by 68 per cent of people who supported Remain last month.