Scotland Yard said three properties - two in Westminster and one in Barnet are being searched along with a number of cars - after two men were arrested on suspicion of terror offences.
Police said that one of the arrests in Westminster took place at a residential address and not near any major landmark.
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Two knives were found at the scene in Islington, North London, and the suspects fled on foot before being arrested.
The violence began after a counter-protester allegedly doused a female rally organiser with pepper spray.
As temperatures climb through the day, the warmest spots are likely to be across western parts of Northern Ireland and western Scotland.