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.
‘Far right and extreme right’
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.
“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.
“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.
Ms Soubry, pro-European MP for Broxtowe and who supports another Brexit referendum, said she objected to being called a Nazi.
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.