Politics has always been a brutal game and its players need thick skins. But it was never supposed to be as brutal as this.

While being interviewed this week the pro-Remain Conservative MP Anna Soubry was interrupted by opponents chanting: “Soubry is a Nazi.”

It wasn’t her first encounter with live, threatening abuse. Outside parliament last month she was surrounded by a group of men shouting “traitor”.

The protesters seemed to feel it was acceptable to intimidate someone who happened to disagree with them.

A new nastiness seems to be pervading our politics.

Now more than 55 parliamentarians have written to the Metropolitan Police demanding action against the most intimidating of the shouters.

It didn’t start this week.

According to the Intimidation in Public Life Review, 56 per cent of candidates in the 2017 general election were concerned about abuse and intimidation.

The EU referendum has caused divisions that have turned ordinary debate into confrontation.

And the fear is that it could lead to far worse.

It reached a horrific and violent point two and a half years ago with the murder of Jo Cox.

The Labour MP for Batley and Spen and mother of two was shot and stabbed to death by a far-right terrorist. And some protesters have since tried to frighten politicians with chilling references to her murder.

Mrs Soubry was threatened by a man who said she should be “Jo Coxed”. The man responsible was jailed for eight weeks.

Catherine Anderson warns that we can’t dismiss such threats as empty ones.

She sees a direct line between abusive language and what happened to Jo Cox. Ms Anderson, from Appleby, is chief executive of the Jo Cox Foundation, set up after the MP’s death to support her belief in a kinder, more tolerant politics.

“Jo Cox’s murder is the clearest example of how insulting and abusive language – online, in print or in-person – can escalate to the point where it becomes physical abuse and assault,” she says. “There is always a danger that what happened to Jo could happen again, as long as the abuse and harassment of people in public life continues to be normalised, accepted and legitimised.

“It only takes one person to move into that more dangerous territory where verbal abuse escalates to physical violence.”

The threats and abuse have been targeted most often at women.

Trudy Harrison’s parents were worried, the MP has said.

Mrs Harrison was elected MP for Copeland in 2017, a year after Jo Cox’s killing, and recalls: “My mum and dad were horrified when I said I was standing, because of my personal safety.”

Other than nasty comments on social media, however, she hasn’t faced intimidation or threats of violence.

“I think the abuse Anna Soubry got is likely to put people off getting involved, particularly women. That is a shame because I’ve found parliament to be a very nurturing, supportive environment..”

John Woodcock, MP for Barrow and Furness said: “There is no place for the harassment, intimidation and threats that are being used against MPs and some journalists.

“The murder of my friend Jo Cox in June 2016 stands as bitter testimony to what can happen when extremist views run out of control and we must guard against any repeat scenario. There is public anger over Brexit and it is up to parliament to find solutions to the problems. MPs will be searching for ways out of the impasse over the weekend and in the Commons from Monday.”

Tim Farron, Liberal Democrat MP for Westmorland and Lonsdale, also stresses that abuse is not the norm.

“It’s important that we condemn this appalling and despicable harassment,” he says.

“However it’s also important to remember that those performing thuggish behaviour outside parliament at the moment represent a very tiny minority of our country.

“A handful of extremists are getting more coverage than they would do otherwise.”

“All the politicians put much of the blame on two factors: social media and the divisions opened up by the Brexit referendum.”