Writing to Met Police commissioner Cressida Dick, the MPs cited “serious concerns” about the “deteriorating public order and security situation”.
It comes after Conservative MP Anna Soubry was verbally abused on Monday.
She was shouted at – including being called a liar and a Nazi – during live TV interviews on BBC News and Sky.
The former minister was later shouted at, called “scum” and jostled as she tried to re-enter the Palace of Westminster.
Ms Soubry later criticised police for not intervening and called for the protesters to be prosecuted under public order laws.
The Met said it is investigating whether any crimes were committed, after having received a third-party report of a public order offence on College Green.
College Green – the area opposite Parliament – is regularly used by media to interview politicians, as well as being a popular site for protesters to gather.
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Labour MP Stephen Doughty coordinated the letter to Met Police chief Ms Dick, which has been signed by at least 55 MPs.
The cross-party group of MPs – which includes those both for and against Brexit – said many of the concerns had been “repeatedly raised” with officers and senior policing staff.
“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,” the letter read.
“We understand there are ongoing investigations but there appears to be an ongoing lack of coordination in the response from the police and appropriate authorities including with Westminster borough policing – and despite clear assurances this would be dealt with following incidents before Christmas – there have been a number of further serious and well publicised incidents today.”
The letter adds that it is “utterly unacceptable for Members of Parliament, journalists, activists and members of the public to be subject to abuse, intimidation and threatening behaviour and indeed potentially serious offences while they go about their work”.
The abuse received by Ms Soubry – which happened while she was interviewed live on the BBC News Channel and also on Sky News – was widely condemned.
Labour’s Mary Creagh said the “really vile, misogynistic thuggery” that had been seen was not an isolated incident.
She pointed to the murder of MP Jo Cox , who was killed in her West Yorkshire constituency by right-wing extremist Thomas Mair in June 2016.
And Commons Speaker John Bercow said he was “concerned” about a “pattern of protest” targeting female MPs and journalists.
Criticism came from different parties and all sides of the Brexit debate – including from high-profile Brexit supporters such as Piers Morgan who called it “disgusting”.
Also on Monday, political commentator Owen Jones published a video to Twitter that he had recorded while being followed and shouted at by a group of protesters outside Parliament.
Ms Soubry has been in touch with the parliamentary authorities responsible for security.
Mr Bercow said he was aware of protests in recent weeks around the Palace of Westminster “involving aggressive and threatening behaviour towards members by assorted groups that have donned the yellow vests seen in France” – a reference to last year’s “gilet jaune” anti-government demonstrations.
While the Met had responsibility for security outside the parliamentary estate, he said, he was keeping a “close eye” on the issue amid concerns that women, in particular, were being targeted.
“I share 100% the concerns expressed and it’s necessary to state very publicly the difference between peaceful protest on one hand and the aggressive, intimidatory and threatening protest on the other.”
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No 10 said the incident was “unacceptable” and MPs “should be free to do their jobs without any form of intimidation”. A Downing Street spokesman said there were laws dealing with public order offences and cases of harassment and threatening behaviour.
The BBC and other broadcasters have set up temporary studios on College Green ahead of the big Commons vote on Theresa May’s Brexit deal on 15 January.
The BBC’s assistant political editor Norman Smith said some MPs had expressed unease privately about being interviewed there given the frequency and vehemence of the protests.
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