Campaigners are marching in central London to demand a final vote on any UK exit deal.
Thousands of people have joined the march to Parliament, on the second anniversary of the UK voting to leave the EU.
The organisers, People's Vote, say Brexit is "not a done deal" and people must "make their voices heard".
It comes as senior Cabinet ministers insist the UK is prepared to walk away from talks without an agreement.
The protest is part of a "summer of action" by campaign groups designed to increase pressure on Theresa May and Jeremy Corbyn.
World War Two veteran Stephen Goodall, 96, led the protesters as they head from Pall Mall for Parliament Square.
Speakers at the demo will include actor Sir Tony Robinson and Gina Miller, who successfully campaigned to ensure the UK could not trigger talks on leaving without the approval of Parliament.
One of the rally organisers, James McGrory from pressure group Open Britain, said there should be "a choice between leaving with the deal that the government negotiates, or staying in the European Union".
"But the most important thing is that this isn't decided just by 650 politicians in Westminster... Brexit is such a big deal [that] it should include all 65 million of us in the country, and that's why people today are marching for a people's vote," he said.
The UK voted to leave the EU by a margin of 51.9% to 48.1% in a referendum held on 23 June 2016.
Britain is due to leave on 29 March 2019, 46 years after it first joined the European Economic Community, the forerunner to the EU.
The government is giving Parliament a vote on the final deal, if one is reached, in the autumn - but it remains unclear what will happen if they reject it.
At the scene
Jennifer Scott, BBC News
EU flags slowly filled Pall Mall all morning, and with chants of "people's vote" echoing alongside drum beats and whistles, the protesters made their way towards Parliament.
This protest is a family affair - young children alongside veterans in wheelchairs, and all ages in between.
One 69-year-old woman called Dodo said she travelled from Derbyshire to protest for the first time in her life.
And I received an eloquent lecture from an 11-year-old on the problems he thought Brexit would bring.
Despite the cheery demeanour of the marchers, the conversations have been less hopeful. One said: "If a million people couldn't march to stop Tony Blair going into Iraq, what chance have we got in getting a vote on the deal?"
These Remainers may not have convinced the government, but there is no doubt from the crowds that thousands are determined to keep trying.
Organisers of Saturday's demo say people "from all walks of life" are present, demonstrating the "growing popular demand" for another vote.
Protester Colin Hopkins, 62, from Ipswich, said: "It's really important to say we don't dispute the decision, but the process and the destination.
"There isn't any agreement on where we want to go with it, even in the government, and we have a right to a second opinion on that."
Leo Buckley, 16, from Hampshire, claimed "Brexit has stolen my future", adding: "It is stealing it economically...I will struggle to find employment and be worse off when I do."
Horst-Dieter Haas, from Germany, has worked as an NHS doctor since 2005 but said he will quit if the UK exits the EU.
"It is already impacting the NHS," he said. "We haven't got enough doctors, nurses, physiotherapists, we don't even have enough money, and that will all be worse if Brexit happens."
Janet Watts, 61, from Suffolk, said she joined the march for her mother - who is from Denmark and arrived in Britain in 1953.
"She had her passport stamped when she got off the boat at Harwich, telling her she could stay," she said. "That has been the same until this referendum happened.
"I think it is disgusting putting families at risk and putting her through this at the age of 83."
This week, the government gave more details on how EU citizens can apply to stay in the UK after Brexit.
EU citizens and family members who have been in the UK for five years by the end of 2020 will be able to apply for "settled status", meaning they can live and work in the UK indefinitely.
Conservative MP Peter Bone - who supports Brexit - said if there were a second vote, the leave campaign would win again.
"The vast, vast majority of people, whether they are Leavers or Remainers, just want us to get on and come out this dreadful European Union super-state," he said.
"There were 17.4 million people that voted for leave and if there are a few thousand in London complaining about it - that doesn't seem to really make much difference."
The government is giving Parliament a vote on the final deal, if one is reached, in the autumn - but it remains unclear what will happen if they reject it.
