Nursing mothers and youths blockaded Google’s London headquarters on Wednesday in protest at the company’s funding of climate deniers, as Extinction Rebellion defied a police order by continuing to stage actions in the capital.

A Guardian investigation revealed last week that Google had made “substantial” contributions to some of the most notorious climate deniers in Washington, despite its insistence that it supports action on the climate emergency.

Mothers of infants held a “nurse-in” outside the company’s offices in King’s Cross and members of XR Youth climbed on top of the entrance to Google-owned YouTube, on the other side of the same building, holding a banner reading, “YouTube, stop climate denial”.

In a letter to YouTube, they said the platform, which has 1.9bn users, had a responsibility to stop hosting “misleading and inherently dangerous” climate denial videos. They pointed out that a recent survey found more than half of teenagers in the US said they got their news from YouTube.

As of 8am on Wednesday there had been 1,642 arrests made over XR protests, according to the Metropolitan police. The rate of arrests accelerated on Monday night after the police imposed a section 14 order in effect banning all protest by the group in London.

Facebook Twitter Pinterest Members of XR Youth protest in front of YouTube offices in central London. Photograph: Ollie Millington/Getty

Lawyers for XR filed an application for an urgent judicial review hearing at the high court. Tobias Garnett, a human rights lawyer working with XR’s legal team, said they would argue that the order was an infringement of the right to protest, was disproportionate, and went beyond the powers given to police by the Public Order Act.

“There’s a general consensus that this is unlawful overreach and that it risks criminalising anyone who seeks to protest about the climate and ecological emergency,” he said. The application was accepted for a directions hearing at 2pm on Thursday.

One of the applicants in the case is Ellie Chowns, a Green MEP who was among those arrested under the new order on Trafalgar Square on Monday night. She said she had not been part of the protests and had been arrested after asking questions of police officers about the legality of their actions.

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She said: “I do plan to go to Trafalgar Square at lunchtime today to stand in solidarity with the Extinction Rebellion protesters because I believe that the right to protest peacefully in a public place is a fundamental cornerstone of our democracy.”

The Met’s deputy assistant commissioner, Laurence Taylor, denied that the force had banned protests and said it had every right to order the demonstrations in Trafalgar Square and elsewhere to end on Monday evening, after nine days. He said “significant disruption” had been caused to London and the Met was under such strain that it had had to draft in 500 officers from across the country.

In spite of the order, hundreds of protesters gathered in Trafalgar Square on Wednesday afternoon for a people’s assembly, asking: “How do we respond to the silence of the government on the climate and ecological emergency in the face of the attempt to silence people with a London-wide ban on our peaceful assembly?”

Police issued attendees with notice of the section 14 and at one stage confiscated a packed-up tent.

Among those who addressed the crowd was George Monbiot, the Guardian environment writer, who went on to block the road at the top of Whitehall along with a number of other activists including Jonathan Bartley, a co-leader of the Green party. Monbiot was later arrested.

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Shortly after he was carried away by police, Monbiot said: “I feel we’ve got to make as much of a stand as we possibly can to prevent ecocide. Business as usual, politics as usual – that is ecocide. It’s the destruction of conditions that make life possible on this earth. I’m standing up against that and I’m proud to be arrested for that cause.”

By 5pm, there were hundreds of people on Whitehall. Watching the action was James Brown, a Paralympic cyclist who had returned to London after being arrested for climbing on top of a passenger plane at City airport last Thursday. He said he had been able to mount the plane because, as a disabled person, he had been given priority access to board before other passengers.

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Brown said he was held in a cell for 67 hours after his protest. “I’m still recovering from that. It was quite an ordeal – especially when as a blind person they won’t give you any access to any reading materials, so it was quite a long and lonely stint.”

Brown said he had become involved with environmental campaigning after his daughter told him of her concerns over biodiversity and the climate emergency. He said he had taken action because the government was not fulfilling its responsibilities to protect people.

He added: “We have to take it in our own hands and do something ourselves and the only means of bringing about radical social change that has been proven time and time again in history is non-violent direct action, and that is the reason I’m taking part in this.”