Three student protesters were arrested on Tuesday after a group occupied a university building in protest at how their university is being run. Police said one was held on suspicion of assaulting an officer, but the demonstrators also accused police of assaulting them.

The protesters said they occupied part of the University of London Senate House headquarters. After being removed by police, they claimed they would continue their protest at a central London police station, where they believed their fellow protester was being held.

Video footage seen by the Guardian appeared to show a police officer punching one hooded protester in the face. In the footage, the demonstrator – who said his name was Tee Jay – fell to the ground and the crowd was pushed back.

Jay, 24, from Hackney, north London, said: "Nothing was said, the police were trying to clear the crowd of people. I turned my back to [the police officer] to kind of walk away, he pushed, I kind of turned round to see who it was – why are you pushing me?

"The punch came and I went straight to the floor, then I got up and left." When asked whether he would take action he added: "What can I do? Look how many of them there are. If I go up to that one officer they'd all just grab me again."

The University of West London mediaproduction student said he was part of the group that occupied part of Senate House.

One protester claimed she was pushed over by officers, who were "punching people indiscriminately". Philosophy student Helen Singh said: "We were walking away from the protest. I was pushed to the ground and my glasses smashed into three pieces."

The University of London Union (ULU), released a statement, which read: "We are still investigating what happened inside, but initial reports indicate that protesters were assaulted by both police and security: thrown to the ground, kicked and punched, and dragged to the ground by their hair."

And ULU President Michael Chessum wrote on Twitter: "Today's eviction … was one of the nastiest, most brutal I've seen on a campus in a long time. Spitting with anger."

In a statement, the students wrote: "Around 60 students staged a peaceful sit-in, issuing 10 demands. Their demands included a halt to privatisation, fair pay for workers and that a controversial plan to close the student union is cancelled."

In a statement released earlier in the day, the students claimed to have "taken over the main management corridor and the vice-chancellor's office in opposition to the way our university is being run and the way the higher education sector as a whole is controlled".

The statement read further: "University of London management is behaving in a disgraceful and unaccountable manner, and we have no choice but to take direct action."

The Metropolitan police said that one person was arrested and held in custody on suspicion of assaulting a police officer. A spokesman said that two others were arrested to prevent a suspected breach of the peace and were later released. The spokesman said that an "approproate number of officers" were sent to reposnd with the demonstration, which began at "around 14.45".

Additional reporting by Dulcie Lee and Ben Jackson