Controversial far-right group English Defence League (EDL) has declared itself "at war" with Islam following the murder of soldier Lee Rigby, 25, by two Islamist extremists on Wednesday.
"What we are seeing is concerted action from individuals across the country. We are really concerned. When you see a wider picture of resentment and retribution, this is telling us its an increasing problem. Something is moving in a very disturbing direction," said Fiyaz Mughal, director of inter-faith charity Faith Matters.
"We can't allow the voices of the far right to become louder than ours in the coming days. All of the Muslim organisations have come out with the strongest possible terms to say there is absolutely no excuse whatsoever, no justification for anything like this," said Julie Siddiqi of the Islamic Society of Britain.
The force has also confirmed that officers are monitoring social media for signs of people trying to exploit the attack to stoke a backlash.