"All these cases are, without exception, self-starting groups and individuals, rather than part of a centrally directed terrorist organisation. The far right threat is not as widespread or systematic as the al-Qaeda-inspired threat and operationally there are vast differences.
"But we also notice that at the same time, at its core, the far right appeals to people who share many of the same vulnerabilities as those exploited by al-Qaeda-inspired extremism.
"It feeds off the same sense of alienation and questions around identity and it has the same ambition to reshape the world in an impossible way. The threat is real, and our response must be effective."
Brokenshire condemned the "worrying phenomenon" of groups like the EDL promoting "offensive, anti-Muslim messages".
It was believed "so-called defence leagues" can provide "gateway ideologies" which enable sympathisers to graduate to hardline extremist activity, the minister said.
Brokenshire said the Home Office counter-terrorism strategy had been updated 18 months ago to include the activities of the far right and said ministers were consulting other European governments over how to deal with the threat.
He said thousands of staff in schools, prisons, social services and hospitals are being trained to spot individuals who are drifting towards extremist views of all kinds.
- Independent