More than 40,000 people signed a petition on the change.Org website saying: "Declare London independent from the UK and apply to join the EU".
While Britain voted 52 per cent in favour of leaving the EU in yesterday's referendum, 60 per cent of Londoners voted for Britain to stay.
"London is an international city, and we want to remain at the heart of Europe," the petition said.
"This petition is calling on Mayor Sadiq Khan to declare London independent, and apply to join the EU," it said.
Khan himself issued a statement on the negotiations for Britain's departure from the EU.
"It is crucial that London has a voice at the table during those renegotiations, alongside Scotland and Northern Ireland," the pro-EU mayor said.
"Although we will be outside the EU, it is crucial that we remain part of the single market," he said.
Another petition entitled "London to remain part of the European Union" garnered over 9,000 signatures on change.Org, saying the vote to leave the EU was "a vital decision that we don't agree with".
A Twitter account @London_Stays was also quickly set up and many people tweeted under the hashtag #londonstays in the wake of the vote.
"Really hoping we're just out, not out out," said Katy Ball. Another user tweeting as @ldn_republic wrote: "No longer British but a Londoner".
Besides London, Scotland and Northern Ireland were the only other parts of the UK where a majority voted in favour of Britain staying in the EU.
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