Organisers claim more than 600,000 protesters descended on the capital on Saturday.
Some 100,000 were initially expected to attend the march, which set off led by young voters and Mayor of London Sadiq Khan at around 1pm.
The People's Vote march set off from Park Lane before ending in a rally in Parliament Square.
Celebrity cook Delia Smith, Dragons' Den businesswoman Deborah Meaden and London Mayor Sadiq Khan were among the speakers at the event, which is being compered by broadcasters Richard Bacon and Mariella Frostrup.
The People's Vote campaign said its stewards estimated the size of the crowd to be around 670,000.
In a tweet, the organisers wrote: "670,000 are on the #PeoplesVoteMarch demanding a #PeoplesVote on the Brexit deal."
Sadiq Khan, the Mayor of London, speaking ahead of his platform appearance, said: "Today will go down as an historic moment in our democracy. A moment when in their thousands, people from every corner of our country and every section of our society will take to the streets - coming to make our voice heard.
"We've heard some complain that a public vote would be undemocratic and unpatriotic. But the opposite is true. There's nothing more democratic - nothing more British - than trusting the people to have the final say on our future.
"The lies, the mistruths and the deceptions of the referendum campaign have now been exposed, and it's clear the will of the people is changing. No one voted to leave the EU to make themselves poorer. No one voted to make life harder for our children and grandchildren. No one voted to see our NHS damaged. And no one voted for the shambles that this Government has created."
In a video message of support, Nicola Sturgeon, the First Minister of Scotland, 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."
Leading speeches in Parliament Square, Delia Smith said people were not fully informed when they voted but now understood "the dire consequences".
"When the vote first happened we weren't fully informed," she said.
Crowd reaching Parliament Square ahead of 570,000 demanding a final #Brexit say on #PeoplesVoteMarch - great to see so many MPs here from across the parties, albeit if from the backbenches pic.twitter.com/HDUGzr6WJc— Chris Leslie (@ChrisLeslieMP) October 20, 2018
"Now we know the dire consequences that can be summed in two words: unmitigated chaos."
She ended by asking MPs where they are and said: "where are you let's be having you," in homage to another famous speech she made.
While Deborah Meaden of Dragon's Den fame said: "If there's one thing business doesn't like its uncertainty."
Ms Meaden explained what she would do if someone came to me and said, 'I will make your family poorer,' as well as damage businesses and cut off ties to a trading partner.
She said she would respond: "I'm out."
The march was led by a group of young voters calling for a second referendum.
The Standard spoke to one group of friends who travelled three hours from Bristol University today.
Alice Beal said: "All of us were under 18 at the time of the referendum."
Nicky Tarran said: "People say the British people have spoken, we haven't."
The march attracted a number of famous faces, including actor Andy Serkis, who was spotted marching with his 14-year-old son Louis and wife Lorraine Ashbourne.
The Lord Of The Rings actor said he is supporting the protest as he believes there should be a second referendum "now that people are more informed".
Despite an expected start time of around 2pm for the speeches, the march was still going well into the afternoon.
The back of the march reached Hyde Park Corner shortly before 4pm, the organisers announced.
Trying to give you a sense of scale of this march. They’ve been marching since 12 and these people still circa ½ mile from destination in Parliament Square. It’s a big thing. #peoplesvotemarch pic.twitter.com/xMexGmItJV— Robert Peston (@Peston) October 20, 2018
Images shared online showed huge numbers of people still marching while the speeches were going ahead in Parliament Square.
Journalist Robert Peston wrote: "Trying to give you a sense of scale of this march. They’ve been marching since 12 and these people still circa ½ mile from destination in Parliament Square. It’s a big thing. #peoplesvotemarch."
While Louise Freya Garner wrote: "#PeoplesVoteMarch - think we’ve missed the speeches but we’re still going!"
And Jim Lorimer tweeted: "This is worse than the M42 on a Friday night - we've done about 100 metres in an hour."
Prime Minister Theresa May has repeatedly ruled out a second referendum, but people travelled from all over the UK to join the rally.
MPs from across all the main political parties are supporting the demonstration.
This includes Labour MP Chuka Umunna, Tory MPs Sarah Wollaston and Anna Soubry, Lib Dem leader Sir Vince and Green Party MP Caroline Lucas.
Meanwhile, former UKIP leader Nigel Farage is leading a pro-Brexit rally at Harrogate Convention Centre later.
The so-called People's Vote is the idea of another vote on the final Brexit deal, which would likely take the form of another referendum.
Many believe the UK is heading for a no deal or bad deal Brexit - which they say is not what the country voted for in June 2016.
The People’s Vote is a grassroots campaign with support from across the political spectrum. It has more than a million social media followers and is growing every day.