Organisers of the “Put It To The People” campaign say more than a million people have joined the march before rallying in front of Parliament.
Marching through central London calling for another EU referendum, as MPs search for a way out of the Brexit impasse.
It comes after the EU agreed to delay the UK’s departure from the EU.
PM Theresa May is coming under pressure to quit after saying she might not put her Brexit deal to a third vote by MPs.
She wrote to all MPs on Friday saying she will ditch plans to put the deal to another so-called meaningful vote if not enough MPs support it.
Downing Street sources have denied reports in the Times newspaper that discussions are underway about a timetable for the prime minister to step down.
Unless her deal is passed by MPs, the UK will have to come up with an alternative plan or else face leaving without a deal on 12 April.
Crowds were told the initial count showed more than a million people had turned up putting it on a par with the biggest march of the century, the Stop the War march in 2003.
London Mayor Sadiq Khan tweeted a video of himself joining demonstrators holding up a ‘Put it to the People’ banner at the front of the march as it began.
He was flanked at the front of the march by Liberal Democrat leader Vince Cable, who tweeted that there was a “huge turnout of people here from all walks of life”.
Meanwhile, a record-breaking online petition on Parliament’s website calling for Brexit to be cancelled by revoking Article 50 has attracted more than 4.3 million signatures.
As the number of signatures on the petition continued to climb, its creator Margaret Georgiadou said she had “received three death threats over the phone”, and a “torrent of abuse” via her Facebook account.