The far right may exploit Brexit tensions with their propaganda triggering rises in hate crime and creating an atmosphere that terrorists can exploit. Britain’s head of counter-terrorism policing is afraid of this.

Neil Basu, who briefs the prime minister and home secretary regularly, told the Guardian he was concerned that far right rhetoric from those lawfully allowed to operate will fuel tensions that spill over, in the same way Islamist propaganda incites terrorism.

He also said a no-deal Brexit leading to a loss of intelligence and data-sharing with Europe would leave its 27 nations and Britain less safe and was of “deep concern”.

Basu said police were working to minimise the damage but operations would be slower and more cumbersome if Britain left without a deal – and ministers knew this.

“My concern is the polarisation, and I fear the far-right politicking and rhetoric leads to a rise in hate crime and a rise in disorder,” he told the Guardian.

He said he was seeing an increase in far right activity from small but vocal groups as the Brexit saga continues, adding: “I am concerned about a small number of individuals trying to make a name for themselves such as Tommy Robinson.”

Basu, who is also Britain’s most senior minority ethnic police officer, said far right rhetoric may not be illegal, but it fuels tensions and he fears its potential effects.

“It generates a permissive atmosphere to people who want to take their argument to more extreme levels,” he said. “There is a difference between being offensive and criminally offensive behaviour, and that is the line we have to monitor.”

Asked by the Guardian about the possible damage from a no-deal Brexit to policing and security, Basu said this could be serious. “It is a very serious flaw in our security arrangements,” he said. “If we have no-deal Brexit, and we could not share that information, and if we lose access to those systems, it will inevitably make the UK and Europe less safe than it is today.”

Basu added: “There will be gaps, and it will be slower and clunkier. We have set up systems to try to deal with a no-deal Brexit. But it will be nowhere near as good as what we have got today.”