The Metropolitan Police has said it will “deal robustly” with the harassment of MPs outside the Houses of Parliament.
It comes after Conservative Remainer MP Anna Soubry was called a “Nazi” by Brexit supporters during a live TV interview.
At least 55 MPs wrote to Met Police Commissioner Cressida Dick to express concerns about security following the abuse on Monday.
Ms Soubry was branded a Nazi and a “liar” during interviews with BBC and Sky on College Green opposite Parliament. She was later verbally abused, called “scum” and jostled as she tried to re-enter the Palace of Westminster.
The MP criticised the lack of police response after officers failed to intervene and said protesters should be prosecuted under public order laws.
College Green is used by the media to interview politicians and is a popular location for pro and anti-Brexit protesters.
On Tuesday, Deputy Assistant Commissioner Laurence Taylor for Met Operations said Scotland Yard was assessing if a crime had been committed and that no arrests have been made.
He said: “We will deal robustly with incidents of harassment and abuse against anyone where that harassment or abuse constitutes a criminal offence.
“Officers in the area have been briefed to intervene appropriately where they hear or see breaches of the law.”
The letter to the Met Police, signed by a cross-party group of MPs both for and against Brexit, was coordinated by Labour’s Stephen Doughty.
It read: “We write to express our serious concerns about the deteriorating public order and security situation in and around the exterior of the Parliamentary estate including College Green.
“After months of peaceful and calm protests by groups representing a range of political views on Brexit, an ugly element of individuals with strong far right and extreme right connections – which your officers are well aware of – have increasingly engaged in intimidatory and potentially criminal acts targeting Members of Parliament, journalists, activists and members of the public.”
House of Commons Speaker John Bercow said he was “concerned” about a “pattern of protest” targeting female MPs and journalists.
Health Secretary Matt Hancock told BBC Two’s Newsnight that the police needed to look “very closely” at the way MPs are treated.
He said: “We’ve got to make sure that MPs and indeed all of us can make these arguments about the future of our country, which people feel very strongly, and even if they disagree, disagree in a reasonable but a civilised way.”
During her interview with BBC presenter Simon McCoy, Ms Soubry said: “I do object to being called a Nazi, actually.
“I just think this is astonishing, this is what has happened to our country. But let’s try and move on and be positive about things.
“I’m also a lass from Worksop, so I don’t get scared by these people or intimidated. I was a reporter during the miners’ strike, so I don’t feel physically intimidated.
“My difficulty is I want to respond and you mustn’t, so I’m really behaving myself.”