Britain faces a new and significant threat from organised far-right "terrorism", the UK's most senior counterterrorism officer said on Monday as he revealed police had foiled four violent plots in the past year.

"The right-wing terrorist threat is more significant and more challenging than perhaps public debate gives it credit for," Mark Rowley, London's assistant commissioner, told reporters.

Rowley said until the last two years, far-right activity was limited to unpleasant protests and hate crimes, with serious incidents limited to the actions of isolated individuals.

The MI5 domestic spy agency are now involved in investigating the far-right and he warned that British groups were seeking links with international groups.

"It's a significant part of the terrorist threat. Right-wing terrorism wasn't previously organised here," Rowley said.

"There are many Western countries that have extreme right-wing challenges and in quite a number of those the groups we are worried about here are making connections with them and networking," he said, declining to give further details because it was a new, live intelligence phenomenon.

Last year, there were five deadly attacks in Britain including one carried out by a man who drove a van into worshippers leaving a London mosque after developing a hatred of Muslims by reading extreme right-wing material online.

The previous year, a Nazi-obsessed loner murdered lawmaker Jo Cox in a frenzied street attack a week before the referendum on the European Union. Since then, Britain has banned National Action and two other spin-off groups, the first extremist right-wing organisations to be outlawed since the 1940s.

'Committed to violence'

"For the best part of 18 months in the UK we have a homegrown, white supremacist, neo-Nazi terrorist organisation that is pursuing all the ambitions of any other terrorist organisation committed to violence," Rowley said.

"That should be a matter of great concern for all of us."

Since the first of the 2017 deadly attacks last March, Rowley said police had foiled four far-right plots, although he said he could not provide details of these as they were subject to ongoing court cases.

To show the overall scale of the threat Britain faced, he said there were 600 investigations currently ongoing involving more than 3,000 suspects.

Over the last three years, arrests had doubled while in the same period some 2,000 people have been referred to the government's counter-radicalisation programme, with a third of these over far-right concerns, he said.

Rowley reiterated British concern about extremists' use of the internet and said he expected technology and internet firms would react to a mixture of persuasion and regulation as the banking sector had done.

He also said it was important that an agreement struck with the European Union so when Britain leaves the bloc in 2019 did not damage relations with their European colleagues.

"Whatever the arrangements, we need something that provides at least a good a platform for cooperation as we have today," he said.