The campaign, 'March for the Future', from Park Lane to Parliament Square was dubbed by the organisers, Open Britain, as the "biggest, loudest and most important" demonstration on Britain's future.
British Prime Minister Theresa May has repeatedly ruled out the prospect of another referendum, saying that the people had already expressed their views in the June 2016 referendum – when the British public voted to leave the EU by a margin of 51.89 per cent to 48.11 per cent.
But the organisers say that "Brexit negotiations are taking us towards a future that nobody voted for".
London Mayor Sadiq Khan is among some of the prominent politicians to throw their support behind the People's Vote campaign, which is demanding a vote on the final deal with the European Union in the form a fresh referendum.
He said, "What's clear is that the only options on the table now from the Prime Minister are a bad Brexit deal, or no deal whatsoever."
"That's a million miles away from what was promised two-and-a-half years ago. In those circumstances, what we demand is that the British public gets a say in whether they accept the outcome of the negotiations, which could be a bad Brexit deal, it could be no deal, with the option of staying in the European Union," Khan added.
Protestors waving placards such as "Breverse", "Exit This Brexit" and "We Want EU" and shouting anti-Brexit slogans marched through central London to gather at the Parliament Square for a rally.
Around 150 bus-loads of people from across the UK reportedly travelled from far and wide for the Saturday's march and rally.
The hashtag #PeoplesVoteMarch began trending on the social media site Twitter as the numbers kept growing through the day.
"Brexit's becoming a dog's dinner. This week's fresh chaos and confusion over Brexit negotiations has exposed how even the best deal now available will be a bad one for Britain," opposition Labour Party leader Lord Adonis, one of the supporters of the People's Vote campaign, said.
"It's a mess that nobody voted for and the reason we are in such a growing crisis is that those cheerleading for Brexit know the promises they made can never be kept," he said.
"The idea that you should have a second referendum would be incredibly damaging – most of all to the trust in democracy from people up and down this country," Richard Tice, founder of the opposing Leave Means Leave campaign, said.
The march comes as the Brexit negotiations hit a major hurdle earlier this week, with the British premier indicating that the post-Brexit transition period may have to be extended to achieve a deal with the EU over contentious issues such as keeping an open border between non-member UK territory Northern Ireland and EU member-state Ireland.
It has caused further turmoil and growing anger within the ruling Conservative Party ranks, with most pro-Brexit ministers opposed to any such extension.
The UK is scheduled to formally leave the EU on March 29, 2019, under the terms of the two-year Article 50 process. The current plan is for a transition period of 21 months to run until December 2021 to smooth the path from Brexit to the UK and EU's future trading relationship.