Some tried logic.
“17 million out of 65 million is not an ‘overwhelming majority’”, read one banner on the anti-Brexit People’s March for Europe, in reference to the EU referendum result.
Others were rather more visceral.
“Pants to Brexit” proved a particularly popular slogan. One lady carried a home-made placard depicting the heads of Brexit Secretary David Davis and Theresa May locked together in a particularly unappealing pair of beige Y-fronts.
One gentleman had decided that for the walk from Hyde Park to Parliament Square, alongside between 15,000 and 20,000 other marchers, he would accessorise his trousers with the most voluminous baggy grey ‘overpants’ he could create.
If the slogans were varied, there was also quite a range among the protesters.
You could find Rod Currie, from Stockton-on-Tees, in the supposedly solid Brexit North-East, rubbing shoulders with Tony Vickers, 70, a harrumphing Home Counties retired lieutenant-colonel.
As his “Stay Angry and Fight Brexit” placard suggested, Mr Vickers, formerly of the Royal Engineers, from Newbury, Berkshire, was indeed cross: “But not with the poor sods who voted Leave. They were lied to, and those poor sods are going to get poorer – while the rich politicians who led the Leave campaign, the ones with dosh, are going to be okay.”
Nor was there any sense – from anyone – that this protest was a futile last stand.
MPs may have been due to vote on Monday on the “Great Repeal Bill”, AKA the EU (Withdrawal) Bill; the referendum may have happened and the negotiations may have been underway, but this march, they all said, could make a difference.
“Anything could happen,” said Mr Currie, 50, an accountant. “Eighteen months [until the end of Brexit negotiations] is a very long time in politics.
“Once people realise the deal they will get is nowhere near as good as what they were told it will be, as more and more small businesses go under because of the falling value of the pound, things might change very quickly.
“They are already changing. The local paper in Sunderland [which voted strongly for Leave] recently published a poll which showed Sunderland would vote Remain now.”
“All it needs,” he added, “is for one-in-50 voters to change their mind and then you have got a 50-50 split between Leave and Remain.
“So we’re still fighting. And the public should be given the chance to vote on whatever Brexit deal is negotiated.”
The Remain cause was far from lost, agreed Christina Murray, 58, a retired legal secretary from Biggleswade, Bedfordshire.
“I went on anti-whaling marches in the Eighties,” she said. “They made a difference. This can make a difference. The mood is already changing. On Facebook, I’ve seen people who voted for Brexit beginning to see the impracticality and undesirability of it.”
‘Boris Johnson’s conscience’ parody sung at anti-Brexit march on Parliament
Ms Murray was on the march with her 22-year-old daughter Imelda. Even if all this protest achieved nothing, “it would still have been worth it”.
“I want to be able to look my grandchildren in the eye and tell them, ‘I fought for your future’.”
It was a common theme.
Anthony Mansfield, 57, came with Kerry Beekmans, 45, and their son Sebastian, three, who was perched on the broad shoulders of his older brother Christopher, 23.
“Seb was born a European citizen,” said Mr Mansfield senior, a train technician from Caterham, Surrey. ”That’s being taken away from him, along with rights like his freedom of movement to work and study in Europe.
“We are watching the pound collapse. In the EU, we have a massive market right next door to us, and we are leaving it.
“I really worry for Seb’s future.”
If there were worries about the future, there were also lessons from history.
Holding a placard reading “Brexit is a weapon of self-destruction”, Kyra von Schottenstein, 60, came to Britain from Austria 33 years ago.
Thirty years ago, she switched from Austrian to British citizenship.
“I am very proud to be British,” she said. “And fighting for the values that made Britain a beacon to the world for years and years and years.”
“We’ve lost that now,” she said wistfully. She is Jewish and had relatives who fled Nazi Austria.
“My objection to Brexit is a moral one. I see a stirring up of hate – towards Poles, towards Lithuanians.
“It’s reminiscent of 1930s attitudes towards immigrants.
“Who are we going to hate next? And who is going to fill all the jobs in the NHS that are currently filled by immigrants?”
These so-called “remoaners” seemed to prefer humour to hatred. As the marchers filed past Downing Street, they were greeted – on the other side of the road to Number 10 – by “Faux Bojo”, a rapping street artist with a remarkable physical and vocal resemblance to Boris Johnson.
“I wrecked the country,” he rapped, poshly. “I put the lies on the bus.”
He had brought his Theresa May puppet along, although she rarely said much more than “strong and stable”.
Nor did Brexit Secretary David Davis escape the ridicule. There was more than one banner with his photo and the verdict of Dominic Cummings, ex-head of the Vote Leave campaign: “Thick as mince, lazy as a toad.”
But it got worse for him at the end of the afternoon when – to a huge cheer – James Chapman, until very recently chief of staff to Mr Davis’ Brexit department, took to the stage.
Mr Davis, said Mr Chapman, the government insider turned ardent Remainer, was a man “without a plan A, let alone a plan B”.
“We are heading to disaster,” he added. “We are heading to a cliff.”
Mr Chapman – who is also one of those to have called Mr Davis, his former boss, a lazy three-day-week man – said the country needed a new political party, the Democrats, to “halt Brexit in the national, geopolitical and economic interest”.
He spoke darkly of the damage Brexit would cause throughout the economy.
“Disgracefully,” he claimed, “they [the Government] have refused to publish their own assessment of the impact of Brexit on over 50 sectors. They say it is because it would undermine [Brexit] negotiations.
“I say it is because of how terrible it would look.”
To a loud cheer, he added the potentially incendiary – and subjective – claim: “This is, in my mind, nothing short of misconduct in public office.”
“We are all European,” he concluded. “For our children, we will continue to fight.”
The plan now is for an ‘autumn of discontent’, including a demonstration in Manchester on 1 October.
“We haven’t gone away,” said Mr Currie. “And we don’t plan to go away.”