Afterwards, the Broxtowe MP criticised police for their failure to intervene and said abusive protesters should be prosecuted under public order laws.
She said there is a ‘very clear distinction’ between peaceful protest and holding MPs to account and recent scenes outside Parliament.
He said the police presence would be increased ahead of next week’s Commons vote on Theresa May’s Brexit deal.
Under Section 5 of the 1986 Public Order Act using threatening or abusive words or behaviour, or disorderly behaviour can lead to criminal prosecution.
Police must balance that against the rights to freedom of assembly and peaceful protest laid down in Articles of the European Convention on Human Rights.
MP of all parties signed the letter to Ms Dick and complained that they had ‘repeatedly raised’ the issue with police but nothing had been done.
Journalists have also been threatened and abused and the Sky New presenter Kay Burley said the abuse was ‘”increasingly vile, aggressive and intimidating”
She said she had changed her route to and from Parliament and now had security protection.
She told BBC Radio 5 Live: “How far does it have to escalate before the police have to take it seriously?”
Labour MP Jess Phillips, told the BBC’s Victoria Derbyshire programme that some protesters were “organised right-wing groups” trying to “intimidate politicians.
She added: “People deserve to be safe at work. 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.”