Lawyers questioned the legality of the ban, made under public order legislation already used to restrict the action to Trafalgar Square, while a number of politicians expressed outrage over the move.
Shadow home secretary Diane Abbott said: "This ban is completely contrary to Britain's long-held traditions of policing by consent, freedom of speech, and the right to protest."
Green Party MEP Ellie Chowns, who was arrested in Trafalgar Square; Green MP Caroline Lucas and shadow policing and crime minister Louise Haigh also spoke out against the move.
Ms Haigh said: "This is a grotesque overreaction and extremely worrying attack on basic civil liberties."
London Mayor Sadiq Khan, who oversees the force, said he would ask for more information over why the ban had been put in place.
Police moved in to clear Trafalgar Square on Monday evening, telling protesters to leave the site by 9pm or risk arrest.
On Tuesday, Metropolitan Police Deputy Assistant Commissioner Laurence Taylor said the protest ban was brought in after "continued breaches" of the condition limiting the demonstration to Trafalgar Square.
He said: "This was an operational policing decision to help us get London moving again.
"After nine days of disruption we felt it is entirely proportionate and reasonable to impose this condition because of the cumulative impact of these protests.
"A significant policing operation continues and we will take robust action against anyone engaged in unlawful protests at locations targeted by Extinction Rebellion."
He said that using section 14 to limit the location and duration of protest action was "not unusual at all", and that the measures had been applied during demonstrations over the jailing of far-right figure Tommy Robinson in August.
Extinction Rebellion activists defied the order and on Tuesday morning. The group's co-founder, Gail Bradbrook, was filmed climbing the entrance to the Department for Transport in Westminster.
The group said other protesters had glued themselves to the building.
Police also dealt with a road block near Baker Street and told a number of protesters camped in Vauxhall Pleasure Gardens to move on or risk arrest.
Activists were seen gathering at Millbank and planned a rally back at Trafalgar Square at midday.
Under the current order, any assembly - classed as a gathering of two or more people - linked to Extinction Rebellion in London is unlawful.
But Mr Taylor said: "We have been very clear with Extinction Rebellion that if they would like to come to us with a proposal for a lawful protest that isn't going to cause the disruption that they've caused to date, then we will happily engage with them and we will happily consider their request."
As of 5pm on Monday, police said there had been 1,445 arrests in connection with the eight days of XR protests in London.
Mr Maugham said on Twitter: "We believe the section 14 Order is invalid - that it amounts to a huge overreach of the statutory power - and likely reflects the enormous political pressure the Met is under.
"It exposes the Met to all sorts of risks - of legal challenges to validity, of civil claims for wrongful arrest with aggravated damages and so on - merely because this Government cannot tolerate peaceful protest."
Allan Hogarth, head of advocacy and programmes at Amnesty International UK, said: "Imposing a blanket ban on Extinction Rebellion protests is an unlawful restriction on the rights to freedom of expression and peaceful assembly.
"This is a heavy-handed and unacceptable move by the Metropolitan Police. Certain disruption to ordinary life for protesting is natural, and it needs to be tolerated."
Human rights lawyer Mr Wagner questioned whether the Public Order Act allows for a city-wide ban on protests.
In a series of tweets, he said: "As things stand, five XR protesters standing on the pavement outside my house would be breaking the law. As would school children with XR banners in a park. The ban seems draconian and extremely heavy-handed even given previous disruption.
"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."