UK politicians have debated a petition signed by more than four million people demanding a second referendum on whether Britain should leave or remain within the European Union.

The debate, which took place in the British parliament's second debating chamber on Monday, did not give MPs legal authority to decide on a second referendum, but demonstrated that the Brexit debate is still raging in the country.

British MPs are obliged to consider for debate any petition which receives more than 100,000 signatures.

"Almost half of those who voted in the June referendum wanted Britain to stay in the EU and some are still marching and protesting," said Al Jazeera's Barnaby Phillips, reporting from London.

"Not many believe a second referendum is likely, but they want Britain to keep close ties with Europe."

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Prime Minister Theresa May has ruled out a second referendum, saying that she is preparing to trigger the formal divorce proceedings that would eventually take Britain out of the club it first joined in 1973.

'Brexit must mean Brexit'

During the June 23 referendum, 17.4 million people, or 51.9 percent of the electorate, voted to leave the EU while 48.1 percent, or 16.1 million people, voted to stay. Some 4.14 million people have now signed the petition calling for a second referendum.

During Monday's debate, David Davis, Britain's newly appointed Brexit minister, made it clear that the UK is leaving the EU.

"There will be no attempt to stay in the EU by the back door," he said. "No attempt to delay, frustrate or thwart the will of the British people. No attempt to engineer a second referendum because some people didn't like the first answer," he said.

Some MPs argued that even discussing a second referendum undermined the will of the British people.

"Brexit must mean Brexit and it is up to every red-blooded democrat, no matter which side they were on before the result was known, to accept the clear electoral verdict and to pull together to deliver it as best we can," said John Penrose, a Conservative politician.

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David Lammy, of the opposition Labour Party, said the public had been "lied to" during the referendum campaign and a second vote on the Brexit deal was the only way out of a "constitutional crisis".

He said the meaning of Brexit was unclear, as were the terms whereby Britain would have access to the European single market.

Just listened to 12 minute statement from David Davis - Secretary of State for @DexEUgov . Still none the wiser about what Brexit means. — David Lammy (@DavidLammy) September 5, 2016

Astonishingly empty statement from Brexit Sec David Davis. No plan, no sense of grip, no detail. It's too important for this kind of drift — Yvette Cooper (@YvetteCooperMP) September 5, 2016

"David Davis has come under some criticism not only from Labour MPs but also from the MPs from the governing Conservative Party," said Al Jazeera's Phillips.

"They were mainly asking for more details. They were saying that the government is badly prepared for Brexit and it still does not have a clear plan for the way forward."

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The Brexit result unleashed immediate political and financial market turmoil in Britain.

The vote has also raised questions about the future of Britain and post-World War II European integration, though the initial economic effect of the Brexit vote has been less negative than was predicted by those who campaigned to remain within the EU.

Several lawsuits have been launched to force the government to accept that parliament should decide on whether Britain should trigger Article 50 of the Lisbon Treaty, which would begin the formal exit process from the EU, rather than allowing the prime minister to decide alone.