Campaigners from all over the UK took part in the demonstration which saw them march to Parliament Square in support of the so-called People’s Vote.
Organisers claimed momentum is growing for another referendum, despite the UK government’s opposition to a vote and its belief that the Leave vote must be respected.
Scottish politicians, including the SNP MP Joanna Cherry QC and the former Scottish Labour leader, Kezia Dugdale, took part in the demonstration.
First Minister Nicola Sturgeon was not there, but sent a video message confirming the SNP’s newly declared support for a People’s Vote.
UK Labour leader Jeremy Corbyn, who has been reluctant to voice support of another poll, was not at the rally, which organisers said had been attended by 670,000 people.
The turnout surpassed expectations, given that organisers had originally estimated that 100,000 people would take part. According to the organisers, their estimate was based on information gathered by stewards on the route. They said that the number had been put to police at the protest, who would not confirm or deny the estimate.
Corbyn’s absence was despite delegates at Labour’s recent conference supporting a motion to keep the People’s Vote option on the table, while acknowledging their preference would be for a general election.
Banners saying “Where’s Jeremy?” were flown by Labour supporters. Corbyn was in Geneva meeting the former president of Chile, Michelle Bachelet, who was imprisoned by the Pinochet regime.
Sturgeon’s message was broadcast from the main stage in Parliament Square where marchers gathered after walking from Park Lane. The SNP leader said: “Let me say this loudly and clearly, if the issue comes before the House of Commons, SNP MPs will support a People’s Vote which includes the option to remain in the EU.”
She added: “The Tory government’s handling of these negotiations has been chaotic, incompetent and shambolic.
“Having spent two years telling us that no deal was better than a bad deal, the Prime Minister is now preparing to pile pressure on MPs to vote for a bad or blindfold deal on the grounds that ‘no deal’ would be catastrophic.
“She is trying to scare the UK into the frying pan out of fear of the fire. It is a scandal and it should not be accepted.”
Speaking on stage, Cherry said the SNP would support a referendum in which Remain was on the ballot paper.
“Scotland voted to Remain and so did Northern Ireland. Despite the fact that I support Scottish independence, we want to see all nations of the UK remain in the UK,” said Cherry.
“I like the EU because it is a union of equals. It is in all our interests to remain in the EU.
“Scotland is looking at being taken out of the EU against her will and I am very, very proud to say that when we know what the Brexit deal looks like, we will support a People’s Vote that includes the option to Remain.”
But the SNP’s calls for another referendum were given short shrift by the Scottish Conservatives last night.
Tory constitution spokesman Adam Tomkins said: “It’s clear that the UK government has to deliver on the result of the EU referendum, and that means Brexit is going to happen.
“Rather than pursue diversionary tactics, Nicola Sturgeon should get on with working with the UK government to get the best deal possible.
“Instead this week she has shown that she is going to persist in trying to use Brexit simply to further her cause for a second independence referendum.”
Cherry appeared on the main platform with Green leader Caroline Lucas, London Mayor Sadiq Khan of Labour, Lib Dem leader Vince Cable and the Remain supporting Tory MP, Anna Soubry.
Celebrity cook Delia Smith and Dragons’ Den businesswoman Deborah Meaden also spoke at the event.
Cable said it was a “tragedy this country is being divided by generation”.
Addressing the rally, he said it was the “majority” of his generation that voted to leave, “taking the freedom” away from young voters.
Receiving cheers from the crowds, he said: “There is no deal better than the one we have now: it is better for Britain and better for Europe.”
Following his speech, Cable added: “I think people have woken up to the potential disaster.
“Even if they negotiate a deal, it’s going to be a bad deal, where we’re going to spend years under European Union rules but have no say in them and beyond that there’s a cliff edge.
“We’ve realised there isn’t a good deal coming out of this and a lot of people are frightened, people are worried.”
Soubry hinted at her displeasure with the leaders of the Leave campaign, like Nigel Farage and Boris Johnson, saying they had “walked away”.
She claimed supporters of the People’s Vote had been “the few” but were “now the many”.
“Where are all the Brexit leaders,” Soubry asked. “They are not taking responsibility for this mess. They have walked away. We will not walk away and we will take responsibility for this mess with a People’s Vote.”
Borrowing language from the Leave campaign, she added: “We will continue to make the case in parliament. We need your help so that the people can take back control of the future of this country.”
Dugdale said: “People from all across Scotland are marching in London to show their support for a People’s Vote. As every day goes by, the harsh reality of a hard Brexit becomes clearer and support for a People’s Vote continues to grow. Brexit is not inevitable.”