Assistant Commissioner Mark Rowley, the Metropolitan Police’s outgoing head of counter-terrorism, told an audience in London that the plots were foiled by security services in 2017.
Speaking two weeks before his retirement, Rowley said on Monday that the threat from far-right groups was “significant and concerning”.
He warned the overall terror threat is “considerable” with over 600 investigations encompassing Islamist, extreme right-wing and other motivations at any one time.
The probes are focusing on more than 3,000 subjects of interest, while security agencies must also keep at least 20,000 individuals who have previously featured in inquiries under review.
The figures are not routinely disclosed but Mr Rowley said it was important to make them public in order to “illustrate the growth of right-wing terrorism”.
Speaking to the media prior to his speech, the senior officer said: “The right-wing terrorist threat is more significant and more challenging than perhaps the public debate gives it credit for.”
Pointing to a shift in the nature of the threat, he added: “Right-wing terrorism wasn’t previously organised here.”
He declined to give details of the four cases for legal reasons but said they “reflect a combination of the organised and the individual”.
His remarks underline the authorities’ mounting concern over the far-right threat, which was laid bare in the murder of Labour MP Jo Cox in June 2016 and the Finsbury Park attack a year later.
“It is important we make these figures public in order to illustrate the growth of right wing terrorism. For the first time we have a home-grown proscribed white supremacist neo-Nazi terror group, which seeks to plan attacks and build international networks. You will agree this is a matter of grave concern,” Rowley said in his speech.
“Islamist and right wing extremism is reaching into our communities through sophisticated propaganda and subversive strategies creating and exploiting vulnerabilities that can ultimately lead to acts of violence and terrorism,” he added.
Rowley noted in his speech an “acute threat from both Islamist and rightwing terrorism” and he described “new and emerging characteristics and the operational challenges it presents.”
Responding to Rowley’s comments, Nick Lowles, chief executive of anti-extremism campaigners Hope Not Hate, said: “Far-right terrorism and violent extremism is on the rise, something that concerns us greatly and which we have long warned the authorities to take note of.
“More worryingly, it is a trend which we fear is going to continue.
“The threat from the British far right is growing and evolving. Many see themselves in a war with Islam and as a result we must be prepared for more terrorist plots and use of extreme violence from the far right for the foreseeable future.”
Last year saw successful Islamist-inspired attacks in Westminster, Manchester, London Bridge and Parsons Green, with one successful far right-inspired attack in Finsbury Park, north London.