About 100,000 people rallied in central London at midday, according to the protest’s organisers.
Many of the marchers carried placards reading “Stop the coup!”
“Boris Johnson, shame on you,” they shouted.
Mr Johnson announced earlier this week that he planned to suspend parliament for almost five weeks this autumn.
Almost all Commons business will be paused from around 9 September until 14 October because of his decision.
Critics claim the government has launched the suspension to block opposition MPs from working to prevent a no-deal Brexit.
But Mr Johnson has said such claims are “completely untrue” and insists the timing of the Queen’s Speech is to bring forward legislation.
“We are bringing forward a new legislative programme on crime, hospitals, making sure we have the education funding we need,” he told Sky News.
The prime minister’s decision has prompted outcry in Westminster and opposition politicians were among the protesters on Saturday.
“It is a fight to protect our democracy – we know what Boris Johnson is up to, it is not very subtle, is it,” Mr McDonnell said.
“He wants to close down our democracy and force through a no-deal Brexit.”
Mr McDonnell said previous generations fought and made huge sacrifices, some giving their lives, in the fight for parliamentary democracy so they could have their say over policies and the future of the country.
“Boris Johnson, this is not about parliament versus the people, this is about you versus the people,” he said.
Some of the London protesters later blocked traffic along Westminster Bridge. “If you shut down our parliament, we shut down your bridge,” they shouted.
Others blocked Waterloo Bridge and traffic near Trafalgar Square.
Scotland Yard said three people had been arrested during the London protests.
Sian Berry, the Green Party co-leader for England and Wales, said Caroline Russell, a London Assembly member, was one of those arrested.
Away from London, protests were held in several other towns and cities.
Organisers said around 5,000 took the streets in Bristol, while several thousand more marched in Manchester.
Protesters filled George Square in central Glasgow to hear speeches from public figures including Jeremy Corbyn.
”I’m proud to be here with all of you supporting that, to say to Boris Johnson no way, it’s our parliament,” the Labour leader said.
“No way do you take us out without a deal – we will stop you and give the people their rights and their say to determine their future.
“Well think on Boris, it’s not on and we’re not having it.”
Earlier on Saturday, Mr Corbyn warned that parliament would have its last chance to stop a no-deal Brexit when the Commons returned next week.
“Yes, it is the chance and we will do absolutely everything we can to prevent a no-deal Brexit and the prime minister taking us into the hands of Donald Trump and a trade deal with the USA,” he said.
“That is the real agenda of the prime minister. There is a lot of work being done in preparation for next Tuesday.”
Crowds more than a thousand strong also gathered for rallies in York, Manchester, Newcastle and Bristol.
One of the smallest and most northerly rallies was held on Orkney, where around 100 people braved the rain to stage a protest in the town of Kirkwall.
Orkney has just 22,000 residents.
Alena Ivanova, from Another Europe Is Possible, said: “Today’s protests are the beginning of something huge – they have been inspiring, full of youth and diversity and energy.”
She said that the daily protests must “grow into the millions” in “the centre of every town in the country.”
Additional reporting by agencies
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