Three cases of alleged harassment outside parliament have been referred to the Crown Prosecution Service after the MP Anna Soubry was repeatedly abused and blocked from entering parliament by pro-Brexit supporters earlier this week.

The cases were sent to prosecutors to “test” whether the behaviour witnessed and filmed went beyond legitimate protest, the Metropolitan police said on Thursday.

Speaking to the London assembly’s policing committee, Sir Stephen House, the Met’s deputy commissioner, said it was for the CPS to decide whether the boundary between demonstrating and stopping people from going about “lawful business” had been breached.

He said: “The crux of the problem is MPs going about their lawful business, but also people lawfully demonstrating. I would underline lawfully demonstrating, that’s what we are asking the CPS to test.”

On Monday the pro-remain MP Soubry, and one of her aides, were filmed being subjected to repeated abuse outside parliament. They also appeared to be briefly blocked from entering parliament.

“There are a number of cases that we have referred to the Crown Prosecution Service in relation to what’s been going over the last few days,” DC House said.

He said he could not go into specifics but confirmed that online abuse was part of the cases involved.

House said: “Social media comments and ongoing dialogue, by a number of individuals, [are] being monitored by the police and do form part of the investigations that we are carrying out.

“There is a distinction between someone putting out misleading information or even fake news, and somebody inciting violence or racial hatred. We are interested in the latter.”

House confirmed that more police officers have been deployed around parliament after the incident highlighted an increasingly rowdy atmosphere over Brexit.

He said: “We have seen, as you would expect in the political situation, an increase in numbers of demonstrators and an increase in the passion exhibited by demonstrators on both sides of the debate over the last few days.

“We have increased the number of officers down there and they are under clear instruction that no member of the public is to be impeded from going about their lawful business.

“Whether it is an MP going into parliament, or anyone else going about their job, people have got an absolute right to go about their lawful daily lives without impediment from someone. That is clearly a balance and clearly outside parliament we are seeing it tested to the extreme limit.”

Asked whether police powers were sufficient to tackle the kind of abuse witnessed, House said: “It is a matter for the home secretary to look at if there is specific legislation that could be put in place around greater protection.

“We are having daily liaison meetings with a number of stakeholders in relations to the issues around parliament, to make sure that we can facilitate people going about their lawful business [so that] specifically working, not just MPs, but aides and others people working within parliament, can get in and out and are not in any way alarmed by what’s going on whilst we try to maintain the ability of people to carry out lawful demonstrations.”