The government will consider giving the police new powers, including the banning of face coverings, following the weekend's anti-cuts march, the home secretary, Theresa May, has said.

May said police could be given the power to ban known troublemakers from attending political demonstrations – similar to how known hooligans can be banned from travelling to football matches.

She told the Commons that 149 of the more than 200 demonstrators arrested during violent clashes with police have now been charged, as she praised officers for learning the lessons of the tuition fees protests.

"The message to those who carry out violence is clear," she said. "You will be caught and you will be punished."

Organisers of Saturday's protest through central London, which culminated in Hyde Park, estimated that between 400,000 and 500,000 people took part in a peaceful rally.

But in separate violent clashes, activists threw missiles at officers in parts of the West End, while others attempted to damage the Olympic countdown clock in Trafalgar Square.

Describing the demonstrators who clashed with officers as "gangs of thugs", May said she "utterly condemned" those responsible for the "mindless" violent behaviour.

She said that "on the whole" the police operation was a success, adding that 56 officers were injured, 12 of whom needed hospital treatment. Fifty-three members of the public were hurt.

May added: "The police might not have managed to prevent every act of violence but they were successful in preventing wider criminality and are now actively engaged in investigating the perpetrators so that they can be brought to justice."

She said that the tactics deployed on Saturday reflect that the Metropolitan police has learnt lessons from the student demonstrations in December, but added that there was more that could be done. "Just as the police review their operational tactics, so we in the Home Office will review the powers available to the police," she said.

"I am willing to consider powers which would ban known hooligans from rallies and marches and I will look into the powers the police already have to force the removal of face coverings and balaclavas.

"If the police need more help to do their work, I will not hesitate in granting it to them."

May said parliament would always back the police "when they do their important work", adding it was necessary they operated within the "right legal framework".

The shadow home secretary, Yvette Cooper, said Labour condemned the "few hundred mindless idiots" responsible for violence.

"In a democracy this kind of violence is no form of political protest," she said. "It is violent assault and criminal damage, it is thuggish behaviour of the worst kind and it must face the full force of the law.

"I welcome the speed with which the police have acted to charge 149 people with offences already. They will have the opposition's support in taking a strong line."