That oft-repeated notion, that a second referendum on Brexit would somehow be an affront to democracy, came to an end on Saturday afternoon. It came to an end beneath the whirring helicopters and the blazing London sun, and above the noble, angry racket of hundreds of thousands of people.

It’s not just that what they were doing was a democratic right in itself, which is to protest, it’s that they came in such large numbers – nearly 700,000, if the organisers’ own estimates are to be believed. It’s that what they made overwhelmingly, unavoidably clear is that they were asking for was the restoration of the most fundamentally important aspect of democracy itself.

“They’ve got to be held to account,” said Ann Murphy, who had travelled from Coventry with her daughter, Samantha, and was there at Marble Arch at noon, waiting to march. “I don’t even know if we’d win. But when politicians make promises they can’t keep, the people have a right to hold them to account for them. If that’s gone, then everything’s gone.”

Spread out before Ann and Samantha was a mile of colour. Blue and yellow, mainly. But red, white and blue as well. And green and red and white. And red and yellow. And black and red and yellow. And red and white.

“It was all a lie,” said Michael Reimer, one of around 20 Poles, waving their Polish flags, a red oblong beneath a white one. “And everybody knew it was a lie. The £350m a week, even the people who voted for that knew it was a lie. It was used as an excuse for a vote against migration.

“Well we are here to show that Polish people have always been here in Britain, contributing to Britain, helping to build Britain.”

The march hadn’t even begun in earnest when Park Lane had to be closed in both directions, not just one. In the build-up to the march, even the organisers of the People’s Vote had been hesitant to refer to their own estimate at the expected size of the crowd, which had been 100,000. Well that number, certainly, was blown away.

Not everyone waved flags. Most carried banners: “David Cameron is a twat – Danny Dyer, 2018” read one.

Editor of the Independent Christian Broughton speaks at the People's March in London

One gang of late-middle-aged men marched down Piccadilly carrying above their heads the broken promises of Brexiteers. “If a democracy cannot change its mind, it ceases to be a democracy – David Davis, 2012.” one said. “No one is talking about threatening our place in the single market – Daniel Hannan, 2016,” said another. That is rather niche.

“There will be adequate food – Dominic Raab, 2018.” Not technically a broken promise, that one. Not yet, anyway.

Under Admiralty Arch, one man stuck his banner into the ground and stopped for a photograph: “Daddy Was Here”.

“I just want them to know I did what I could,” he said to the person who had asked if he could take it.

Another showed a large map of Europe, with the words: “Don’t Take Away My Free Movement”.

A sharp reminder of the fundamental imbalance of the referendum. The Remain campaign did not fight to take anybody’s rights away. Only the Leave side did that, and they won. That people will not sit down and accept the diminishing of their lives, their opportunities and their country should not come as any surprise. Not least as there’s nothing democratic about it. It’s straightforward majoritarianism.

“People say, oh, ‘Nobody voted for this mess,’ don’t they?” said Dawn Smith, a student in a blue and yellow facepaint, marching with around 30 of her friends. “But you don’t know do you? Maybe they did. But we’re not marching for Remain, we’re marching for a second referendum. People should be able to say, ‘Yes, this is what we voted for. This is what we wanted.’ All the broken promises, all the lies. If that’s what people want they should be given the chance to say so.”

By the time they made it to Parliament Square, the marchers were backed up all the way along Whitehall, past the Treasury, past the Foreign Office, past 10 Downing Street.

One woman, with not too bad a voice, had set up a full PA system opposite the gates to 10 Downing Street and was belting a re-worked version of a Phil Collins classic. “I’ve been talking to Theresa, and she knows I’m right.”

In the build-up to this march, one of its leaders, Alastair Campbell has been repeatedly asked the same sharp question. In 2003, more than a million people marched past 10 Downing Street, telling Tony Blair not to go to war in Iraq. That advice was not taken.

Mr Campbell has had a sharp answer: that the decision was put the House of Commons and a majority voted for it. Whatever Brexit deal Theresa May gets, such a course of action may very well not be open to her.

But the sharpest answer is a different one: that he should have listened. That, with hindsight, the sheer size of the gathering masses should have been sufficient to persuade them to think again.