Senior officers say it will be a "spectacular" that is designed to kill. The counter-terrorism unit has redeployed officers to increase its monitoring of the extreme right's potential to stage attacks.
Commander Shaun Sawyer told a meeting of British Muslims concerned about the danger to their communities that police were responding to the growing threat.
Sawyer said of the far right: "I fear that they will have a spectacular... they will carry out an attack that will lead to a loss of life or injury to a community somewhere. They're not choosy about which community."
He said the aim would be to cause a "breakdown in community cohesion".
Sawyer revealed that the Met commissioner, Sir Paul Stephenson, had asked the counter-terrorism command, SO15, to examine what the economic downturn would mean for far-right violence. The assessment concluded that the recession would increase the possibility of it.
Sawyer told the meeting last Wednesday that more of his officers needed to be deployed to try to thwart neo-Nazi-inspired violence. He said the terrorist threat posed by al-Qaida remained the unit's priority, but said of its far-right section: "It is a small desk ... we need to grow that unit." Sources have told the Guardian that while they believe the neo-Nazi terrorist threat has grown, they have no specific intelligence of an attack.
"There is an increased possibility of violence from the far right. There is a trend," said one senior source, adding that the ideology of the violent right was driven by "people who don't like immigration, people who don't like Islam. We're seeing a resurgence of anti-semitism as well."
The meeting at which Sawyer spoke was staged by the Muslim Safety Forum, whose chair, Abdurahman Jafar, said: "Muslims are the first line of victims in the extreme right's campaign of hate and division and they make no secret about that. Statistics show a strong correlation between the rise of racist and Islamophobic hate crime and the ascendancy of the BNP."
It is a decade since an extreme rightwing terrorist has used bombs to claim lives in Britain. In 1999, David Copeland struck three targets in London. His attack on a gay pub in Soho, London, killed three people and left scores injured. It followed attacks against the Muslim community in Brick Lane, east London, and the bombing of a market in Brixton, south London.
The senior source said: "When Copeland attacked we did not have the religious tensions with the Muslim community. What kind of schism would a Copeland-type event cause now?"
The far-right threat to Britain's Jewish communities is monitored by the Community Security Trust, which says attempted terrorist violence by neo-Nazis has increased in the past few years. It says nine white men have been "convicted of offences involving explosives, terrorist plots, violent campaigns or threats to carry them out".
David Rich, of the CST, said: "There's no one directing people, it's a mindset" – a reference to the easy availability of extremist right-wing material and information about making bombs.
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