Some demonstrators Saturday explained they were not necessarily against Brexit but wanted citizens to have another vote on any final deal that Prime Minister Theresa May negotiates in coming months.
"If it's a no-deal or a bad deal, we should get a chance to look at it - because it is the decision of a lifetime," said Peter Davis, 45, an office manager from London, standing at Parliament Square.
Others wanted a redo referendum.
When asked whether Brits didn't already settle the matter two years ago in their historic decision to leave the European Union, Davies answered, "I don't know if people really knew what we were voting on."
Others in the crowd said they supported Brexit, but a soft, gentle, friendly Brexit in which London would have more say over budgets or migration, but might stay in Europe's customs union or single market - allegedly two red lines for May.
Victoria Lewis, 55, a math teacher from Brighton who wore a blue T-shirt that read "Citizen of Europe," came out to rally "because I have three children and they need to be part of Europe. Humanity is about us cooperating, not putting up false barriers."
"It's no accident there hasn't been a war in Europe for 70 years." she said. "It's because we have been talking to each other and cooperating."
There are growing fears that Britain will "crash out" of the European Union, with no agreement on future relations and trade - bringing about chaos.
This week, the executives of the aircraft manufacturer Airbus, which directly employs 14,000 people in the United Kingdom and supports another 100,000 in its supply chain, warned May about leaving the European bloc without a good deal.
"Put simply, a no-deal scenario directly threatens Airbus's future in the UK," said Tom Williams, the company's chief operating officer, on BBC.
"We are seriously considering whether we should continue that development or we should find alternate solutions," Williams said about plans to manufacture airplane wings in Britain.
BMW's top executive Ian Robertson told reporters that UK car manufacturing was hurtling toward a cliff and that his company needs to know by the end of the northern summer what's what - and not in October, as May plans. BMW employs about 8000 people in Britain.
John Neill, chief executive of Unipart, a car parts supplier that employs 6000 people in Britain, told the Financial Times, that carmakers would "find it very difficult to survive in the long term" if May chose a hard Brexit.
May and her Cabinet are divided over the best way forward on Brexit - and the Prime Minister has delayed, yet again, a clear declaration on what future relations with Europe should be.
In an editorial in the Sun tabloid this weekend, Britain's Foreign Secretary Boris Johnson warned May that those who voted for Brexit "don't want some bog roll Brexit - soft, yielding and seemingly infinitely long" he said, deploying slang for toilet paper.
Recent polling shows a stubborn split among respondents - though there appears a slight tilt against Brexit. In the last round of surveys by YouGov, 46 per cent believe leaving the European Union was the wrong decision, while 43 per cent think it was correct.
Campaigners against Brexit want another referendum, which they call a "people's vote," to bail on leaving.
Brexiteers say that the vote has already been held and that the "people's will" should be respected. This is the prime minister's position, too.
