Heated rhetoric and name-calling by politicians arguing over Brexit risk triggering violence on the streets and attacks on public figures, experts from policing and mental health backgrounds have warned.

They include the co-founder of a special unit, set up to advise the Home Office on the threat to MPs and others, who said constituency offices remained “wide open” to potential attacks despite a greater appreciation of the threat since Jo Cox’s murder.

Reductions in police numbers and underfunded health services were also cited by Dr David James as problems when it came to identifying and intervening in the cases of mentally ill people who could pose threats to MPs.

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“As regards money, there is now no ‘national’ health service, and few psychiatric teams to whom one can refer mentally ill people who are presently a risk,” said James, a consultant forensic psychiatrist who co-founded the Fixated Threat Assessment Centre (FTAC).

Sir Peter Fahy, a former chief constable of Greater Manchester police, said: “When norms of courtesy are damaged, there is a ripple effect through society. It gives succour to extremists and there is a danger that some take that to violent conduct.”

James and Fahy, formerly the national police lead for the Prevent anti-radicalisation programme, spoke after furious exchanges in the House of Commons on Wednesday, during which Boris Johnson dismissed MPs’ concerns over the language he was using as “humbug” and repeatedly referred to the Benn Act seeking an extension to the Brexit deadline as “the surrender bill”.

Fahy, who was also the vice-president of the National Police Chiefs’ Council, said: “If that conduct is to besmirch and aggressively attack and question their [opponents’] motives, the danger is that coarsens the language … and gives some permission to do something more extreme.”

A second potential damaging effect was cited by Fahy, who said such rhetoric could “affect trust in a collective society”.

He added: “If people feel the government or establishment is not legitimate and is not being effective, that can create an idea everything goes and I don’t need to obey the norms. For policing to be effective you need a cohesive society, where people see the system as legitimate and effective.”

Hundreds of people have been detained under the Mental Health Act after referrals from FTAC since it began operations in 2006. The centre – a joint NHS/police unit within Scotland Yard – assesses and manages the risks from individuals who harass, stalk or threaten public figures, and was set up initially doing research for the Home Office into the harassment of members of the royal family.

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James, who is no longer directly involved in the centre, was candid about the extent and the number of threats to MPs, which he said went up and down depending on how politicians, and particularly rightwing Brexiters, were “upping the rhetoric”.

He added: “Most of this stuff would not lead to anything further. But some loners may be stimulated to act and given permission to do so by the inflammatory rhetoric of politicians. Even where no escalation is likely, the psychological trauma caused by all this stuff risks impairing the function of the democratic process.”

A tendency among some MPs in the past to view aggressive behaviour towards them as something that goes with the job had changed, said James.

“If anything, some MPs are overreacting – in that they are reporting abusive messages and mistaking them for threats. There is closer cooperation now between local police and constituency offices. There were stories previously of forces who were unable to name their local MPs,” he said.

“However, it is constituency offices and [behaviour such as MPs] walking around the constituencies themselves that remains wide open to nasty events. After all, you can’t protect everyone. You rely upon social standards and sets of decency as your first line of protection.”