Speaker John Bercow has described the abuse and harassment of MPs outside Parliament as "a type of fascism" and called for a change of policing policy.
He said recent incidents, including Tory MP Anna Soubry being verbally abused on Monday, were "intolerable".
At least 115 MPs have called on police to improve their response to abusive protesters outside Parliament.
The Metropolitan Police has said it is ready to "deal robustly" with any instances of criminal harassment.
Deputy Assistant Commissioner Laurence Taylor said the force was assessing whether any crimes had been committed, following a third-party report of a public order offence on College Green, opposite the Houses of Parliament.
He said Scotland Yard will be "enhancing the policing presence" in the run-up to next week's vote on Theresa May's Brexit deal.
Revised advice was issued to MPs by Parliament security on Tuesday.
Meanwhile, a man has been arrested on suspicion of trespassing after he tried to get into Parliament.
Armed officers arrested him at about 19:20 GMT on Tuesday after he got through Carriage Gates, at the entrance to the Houses of Parliament. He was taken to a police station, the Metropolitan Police said.
The incident is not being treated as terror-related.
The BBC has no plans to stop broadcasting from College Green but does not intend to report from there every day.
A BBC spokeswoman said: "We are working closely with authorities and other broadcasters to ensure the safety of our reporters and interviewees at all times."
Ms Soubry was shouted at - including being called a liar and a Nazi - during live TV interviews on BBC News and Sky.
The former minister - a supporter of a fresh Brexit referendum - was later called "scum" and jostled as she tried to re-enter the Palace of Westminster.
She criticised police for not intervening and called for the protesters to be prosecuted under public order laws.
Section 5 of the 1986 Public Order Act means that "threatening or abusive words or behaviour, or disorderly behaviour" might be deemed a criminal offence.
But Article 10 (right to freedom of expression) and Article 11 (right to freedom of peaceful assembly and to freedom of association) of the European Convention on Human Rights contain the rights to peaceful protest.
College Green is regularly used by media to interview politicians, as well as being a popular site for protesters to gather.
Ms Soubry told the BBC she had "no problem with people protesting", saying this was a "very small group of far-right extremists who just want to undermine democracy".
The MP for Broxtowe said: "There is a very clear distinction between peaceful, lawful protest and robust debate - holding MPs to account, and it can be face to face - and some of the scenes we have seen in the last six weeks here at Parliament."
The cross-party group of MPs who have signed the letter - 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, co-ordinated by Labour MP Stephen Doughty, 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."
The letter said there appeared to be a "lack of co-ordination in the response from the police and appropriate authorities".
Sky News presenter Kay Burley said the "increasingly vile, aggressive and intimidating" abuse had forced her to change her own route to Parliament and she now had to have security protection.
She told BBC Radio 5 Live she had been interviewed three times by the police about the situation, but the protesters knew their rights and what they could and couldn't get away with.
But she added: "How far does it have to escalate before the police have to take it seriously?"
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.
Commons Speaker John Bercow said he was "concerned" about a "pattern of protest" targeting female MPs and journalists and called it a "type of fascism".
In his letter to the Met Police chief on Tuesday, he said he recognised it was "a difficult job striking the balance between allowing peaceful protests and intervening when things turn sour".
But he added: "It's one thing demonstrating from a distance with placards, or calling out slogans - and another, where the protester invades the personal space of a member, subjects him or her to a tirade of menacing, racist, sexist and misogynistic abuse, and follows them back to their place of work."
Labour MP Jess Phillips, who has previously spoken out against online abuse, told the BBC's Victoria Derbyshire programme that some protesters were "organised right-wing groups" trying to "scare our politicians into making decisions based on fringe views".
"People deserve to be safe at work," the Birmingham Yardley MP said. "I didn't come here to be bullied by far-right bullies, far-left bullies, or anyone, we came here to do what we felt was best."
Also on Monday, political commentator Owen Jones published a video on Twitter that he had recorded while being followed and shouted at by a group of protesters outside Parliament.
Last month, a video emerged of prominent Brexiteer Michael Gove being accosted by a protester dressed as Santa as he walked to Parliament.
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.
By Dominic Casciani, BBC home affairs correspondent
A recognisable figure in the group that surrounded Anna Soubry on Monday is online far-right campaigner James Goddard.
He says there can be no peace while Islam exists in the West and that the establishment is riven with paedophiles. He told police outside Parliament they were "fair game" and "if you want a war, we will give you a war".
Mr Goddard emerged as a DIY far-right campaigner last year as he began to gather followers after campaigning in support of the then-jailed anti-Islam activist, Stephen Lennon aka Tommy Robinson.
Before the incident at Parliament involving Ms Soubry, he'd been helping to organise France-style "yellow vest" protests - including attempts to block bridges in London.
Mr Goddard relies on donations from his followers - he frequently runs crowdfunding appeals for his campaigns.
On Tuesday evening, Facebook confirmed it has closed his account.
"We will not tolerate hate speech on Facebook which creates an environment of intimidation and which may provoke real-world violence," said a spokesman. Minutes later, his separate Paypal crowdfunding page disappeared too.
No 10 said the incident was "unacceptable" and MPs "should be free to do their jobs without any form of intimidation".
The BBC and other broadcasters have set up temporary studios on College Green ahead of the Commons vote on Mrs 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.