Extinction Rebellion activists are continuing protests despite a London-wide ban by police.
The group says it has taken initial steps towards a judicial review of the ban. Lawyers and politicians have also criticised the move.
Meanwhile climate change protesters targeted the Department for Transport and MI5 on Tuesday morning.
A government spokeswoman said protests “should not disrupt people’s day-to-day lives”.
Extinction Rebellion’s co-founder, Gail Bradbrook, was arrested after climbing on to the entrance of the Department for Transport on Tuesday morning. Police also cleared further protesters from outside the building.
Activists have also been arrested on Millbank outside MI5’s headquarters, where a small group had gathered. Two men briefly sat in the middle of the road before being moved by officers.
On Monday evening, the Metropolitan Police began clearing protesters from Trafalgar Square following the announcement of a ban on the protests.
Under Section 14 of the Public Order Act, the force had imposed conditions requiring activists to stop their protests in central London by 21:00 BST on 14 October or risk arrest.
The Metropolitan Police said that the ban was imposed after “continued breaches” of a condition limiting the demonstration to Trafalgar Square.
Extinction Rebellion said it had taken the “first steps” towards a judicial review of the Met’s “disproportionate and unprecedented attempt to curtail peaceful protest”.
“Our lawyers have delivered a ‘Letter before Action’ to the Met and asked for an immediate response,” a statement read.
Tobias Garnett, a human rights lawyer working for the movement, said the letter warned police to withdraw the order.
He said the campaign group had given the police a deadline of 1430 BST to respond, or it would file a claim in the High Court.
“We will be looking for an expedited hearing either today or tomorrow morning,” he added.
Speaking to the Victoria Derbyshire programme, Extinction Rebellion campaigner and former Met Police officer Paul Stephens said: “Police are being really sloppy with the law, and it won’t stand up in court.”
Mayor of London Sadiq Khan has said he is “seeking further information” about the decision to impose the ban and why it was necessary.
“I believe the right to peaceful and lawful protest must always be upheld,” he said.
A spokeswoman for the government said the UK was “already taking world-leading action to combat climate change”.
The statement added: “While we share people’s concerns about global warming, and respect the right to peaceful protest, it should not disrupt people’s day-to-day lives.”
Home Secretary Priti Patel tweeted that “supporting our [police] is vital” and accused the Labour Party of supporting “law breakers”.
‘Overreach of powers’
Meanwhile, lawyers have also questioned whether the ban by police is legal.
Anti-Brexit barrister Jo Maugham QC said the move was “a huge overreach” of police powers, while human rights lawyer Adam Wagner described it as “draconian and extremely heavy-handed”.
Mr Wagner added in a tweet: “We have a right to free speech under article 10 and to free assembly under article 11 of the (annex to the) Human Rights Act. These can only be interfered with if the interference is lawful and proportionate. I think the police may have gone too far here.”
Shadow home secretary Diane Abbott tweeted: “This ban is completely contrary to Britain’s long-held traditions of policing by consent, freedom of speech, and the right to protest.”
Allan Hogarth, of Amnesty International, issued a statement saying the ban was “an unlawful restriction on the rights to freedom of expression and peaceful assembly”.
A number of demonstrations have been staged across the capital by Extinction Rebellion, which is calling on the government to do more to tackle climate change.
The protests were due to last two weeks and have led to more than 1,400 arrests.
The Met said there had been 1,457 arrests by 08:45 BST on Tuesday, in connection with the nine days of Extinction Rebellion protests in London.
Last week, the Home Office confirmed to BBC News that it was reviewing police powers around protests in response to recent demonstrations.
What are the rules around protests?
Police have the powers to ban a protest under the Public Order Act 1986, if a senior officer has reasonable belief that it may cause “serious disruption to the life of the community”.
Police are also under a duty to balance the task of keeping the streets open with the right freedom of assembly under the Article 11 of the Human Rights Act 1998 and freedom of expression, under Article 10. These rights are not absolute – the state can curtail them.
However, the BBC’s home affairs correspondent Dominic Casciani said: “The test, if and when it gets to a court battle, is whether police action was proportionate to threat and only what was strictly necessary.”
By law, the organiser of a public march must tell the police certain information in writing six days in advance.
Police have the power to limit or change the route of the march or set other conditions.
A Section 14 notice issued under the Public Order Act allows police to impose conditions on a static protest and individuals who fail to comply with these can be arrested.