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Sadiq Khan said there was real concern among business leaders that companies could leave the City.
It comes as the mayor of Frankfurt told BBC London his city's "arms and our doors are open".
London-based financial technology firm Transferwise said it had been courted by several European countries already.
The company's chief executive Taavet Hinrikus said his company was being courted by Ireland and Switzerland among others.
A spokesman for Transferwise, which processes international currency payments, said moving away from London was "not something the firm was actively talking about".
The spokesman added that Transferwise had chosen to make its base in London and that the company "hoped it could make that work".
But he added that businesses needed greater certainty in order to operate successfully.
Mr Khan told BBC London there was genuine concern among leading figures in the City he had spoken to, including Bank of England governor Mark Carney and London Stock Exchange chief executive Xavier Rolet.
"There is a concern that if we don't have access to the single market, if we haven't got passporting of financial services, that could lead to businesses leaving London to go to those cities where there is access to the single market," he said.
The latest government figures estimate the FinTech industry - financial technology - generates about Â£20bn in annual revenue.
And Mr Khan said it was just one industry being targeted by other European centres.
"The mayor of Milan was here this week, I met with him, Why was he here? He wants to pinch our business. Who can blame him?
"The mayor of Paris and the deputy mayor have already said they're rolling out the red carpet to invite businesses to come to Paris. Why wouldn't they?"
Dublin-based investment group IDA Ireland is planning an advertising campaign in the autumn highlighting Ireland's tax regime, its proximity to London, and the shared language to businesses thinking about relocating.
Peter Feldmann has had a busy few days. Frankfurt's lord mayor has been celebrating the birth of his second daughter on Monday night.... and who knows perhaps a new lease of life for his city too.
He greets us in the grand surroundings of the Kaiser Hall in Frankfurt's equally grand City Hall and can barely contain his smiles.
Opportunity, he believes, has come knocking with the UK's decision to leave the EU.
"Our arms and our doors are open," he tells me when it comes to London businesses big and small that are looking to relocate.
At a business meeting the day after the Brexit vote, people cheered and clapped him saying: "here is the winner from Brexit".
In the coming weeks his team will fly to London to make their case. Frankfurt already has a video selling its wares and a team of English speakers taking calls from businesses.
Mr Khan told the BBC: "London is open: we're open for talent, we're open for business, we're open for investment. The government has got to help me do my job as mayor to make sure that we send that message out loud and clear around the country, around Europe and around the world.
"We've got competitors who want to pinch that business, we've got competitors who want businesses to go to their cities. We cannot allow that to happen."
Business and Energy Secretary Greg Clark said giving businesses the certainty they need to plan for the future is a "key priority".
"That's why we are working closely and collaboratively with businesses across all sectors to ensure that the UK remains the best place in the world to do business," he said.
A minute after the Brexit vote was announced Frankfurt launched a website and phone line in a bid to encourage businesses that want to remain in the single market to relocate there.
The mayor of Frankfurt, Peter Feldmann reiterated that invitation on Thursday, telling BBC London: "If you want to become rich, if you want to stay wealthy, you should have a [department] in Frankfurt.
"If you want to become isolated and see from a binocular perspective what is going on in the world, stay in London."
Meanwhile, German business development group Berlin Partner said earlier this week that at least 10 London start-up firms had made enquiries about moving to Berlin since the UK voted to leave the EU last month.
Berlin is attempting to woo London's FinTech industry and, like Frankfurt, has stepped up efforts to promote itself as a more affordable and creative alternative to other cities.
At London's FinTech conference earlier this week, Berlin Partner director Stefan Franzke said: "The most concrete enquiries are coming from London FinTechs. They are considering a move to Berlin so as not to lose access to the European single market."
Berlin's senator for economics, technology and research, Cornelia Yzer, has sent hundreds of letters to UK businesses and earlier this week travelled to London Fintech Week to lobby start-up founders.
She told BBC London: "We are an international community and that's why companies will find talents there they need. So welcome, and we'll bring all hurdles down, we'll offer programmes for relocation. So pick up the phone talk to me and my team and relocate to Berlin."
More than 100 companies have already been in touch with her team since the Brexit vote, she says, and in September they will open an office in London.
But Mark Boleat policy chairman at the City of London Corporation said he remained confident London would continue to be the world's leading financial centre.
"While some European cities might look to entice businesses and jobs to the continent, we have so many strengths which make us such an attractive place to do business," he said
"Highly skilled workers, excellent infrastructure and a stable regulatory system are but some of those, and crucially the capital is a place where people want to work and live."
Asked whether London had been ill prepared for the Brexit result, Mr Khan said that was now important was that London now dealt "with the hand that we've been given".
Mr Khan said it was "really important that we explain to the government it's in the country's interest for them to listen to us."
"Uncertainty isn't helping."
The mayor of London has warned of the growing threat of foreign cities trying to steal business from the capital, one month on from the EU referendum.

Jacobus van Nierop, 51, took out healthy teeth and caused horrific injuries to the patients in the small town of Chateau-Chinon.
Van Nierop was banned from practising dentistry and fined â‚¬10,500 ($11,900).
Van Nierop fled to Canada when suspicions arose and strongly fought against extradition to France in 2014.
The court in the central French town of Nevers heard that patients had suffered broken jaws, recurrent abscesses and septicaemia from van Nierop's work.
Van Nierop was arrested in France in June 2013, after the number of his victims grew to 120.
However, he fled the country before his trial was due to start in December that year.
He was tracked to a small town in the Canadian province of New Brunswick and arrested under an international warrant.
The BBC's Hugh Schofield in Paris says that van Nierop was many people's worst nightmare.
Like many parts of rural France, Chateau-Chinon is badly served for medical provision, our correspondent says, adding that locals initially seemed delighted by the hard-working and smiley dentist, a larger-than-life character who witnesses said was rarely seen without his "big 4x4, a big dog and a big cigar".
But then the horror stories began. People said they had teeth ripped out for no reason - they were given heavy anaesthetic, then left with abscesses and infected gums.
A Dutchman dubbed the "dentist of horror" has been sentenced to eight years in France for mutilating the mouths of more than 100 patients.

The 24-year-old winger, whose current deal ends at the end of 2016, has turned down a four-year contract offer.
"He should be a regular fixture in the starting line-up every single week," Bonner told BBC Scotland.
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"I would love him to stay at Celtic because there is no better place if you are playing really well."
Forrest came through the youth ranks at Celtic, making his debut in 2010.
The Scotland midfielder has scored twice in 32 appearances this season.
Norwich and Queens Park Rangers are interested in the player but Bonner, who made over 640 Celtic appearances, thinks Forrest should remain where he is and prove himself.
"James is a wonderful talent," said the former Republic of Ireland keeper, who spent his entire club career at Celtic Park. "He has great ability on the ball.
"The problem with James is inconsistency. He's had his injuries, but for me it looks like a mental thing.
"As soon as you walk on to the pitch you've got to make things happen, especially if you're playing at home for Celtic, especially if you're playing out on the wing - because some great players have played in that position over the years.
"There are times when I'm surprised he's not in the team and there are times when he is that I'm surprised he's not effective enough.
"When he is effective, there's nobody better at getting the fans up out of their seats.
"But it's up to him, no one can do it for him."
Forrest has made 13 Scotland appearances, starting on seven occasions.
"He is still a young man and he also has an international career to think about," added Bonner, who won 80 caps.
"The only way you're going to progress yourself for Scotland is to be playing every week and being successful and he can do that with Celtic.
"Sometimes, going away for more money might not be the right decision.
"Maybe he feels a wee bit stagnated and thinks he needs a change of scenery just to kick on. That can happen, of course."

James Forrest has been urged to stick with Celtic and "become a main player" at the Scottish champions by the club's former goalkeeper Pat Bonner.

