Fears of a prolonged backlash against Muslims have intensified after dozens of Islamophobic incidents were reported in the wake of the murder of the British soldier Lee Rigby in south London.

The Tell Mama hotline for recording Islamophobic crimes and incidents recorded 38 incidents over Wednesday night, including attacks on three mosques, with more reported on Thursday.

The Metropolitan police put 1,200 more officers on the street on Thursday, with extra patrols deployed to mosques and religious sites as far-right groups reacted to the tragedy.

The Tell Mama co-ordinator Fiyaz Mughal, from Faith Matters, said the service usually recorded three or four incidents on an average day, but the spike after Wednesday's killing reflected simmering resentment against Muslims and was unlikely to fizzle out.

"What we are seeing is concerted action from individuals across the country," he said. "We are really concerned. When you see a wider picture of resentment and retribution, this is telling us it's an increasing problem. Something is moving in a very disturbing direction."

A 43-year-old man was being questioned on Thursday on suspicion of attempted arson and possession of an offensive weapon at a mosque in Braintree, Essex. The local MP, Brooks Newmark, tweeted that the man was carrying "knives and an incendiary device".

Another man was held on suspicion of racially aggravated criminal damage after Kent police were called to an incident at a mosque in Gillingham, Kent.

Graffiti attacks were reported on mosques in Bolton, where cars parked outside were also vandalised on Wednesday night, and in Cambridge on Thursday.

The incidents compiled by Tell Mama, which monitors news feeds and social media as well as taking calls from the public, included seven incidents of Muslims being abused – including being spat at or threatened in the streets – another five mosques being threatened, and dozens of other online threats.

On the "True British Patriots" Facebook page, there were calls for mosques in Watford in Hertfordshire and Morden, south London, to be burned down.

The incidents came despite prompt and unequivocal condemnation of the murder by leaders of Muslim groups, including the Muslim Council of Britain, the Ramadhan Foundation and the Islamic Society of Britain, as well as individual Muslims, a number of whom took to social networks to express their disgust.

"We can't allow the voices of [the British National party leader] Nick Griffin and the far right to become louder than ours in the coming days," Julie Siddiqi, of the Islamic Society of Britain, told Radio 4's Today programme. "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."

But Mughal warned: "I think the damage has been done." He said his own address had been posted on Twitter, with users invited to shoot him. In response to the heightened tension, he has contacted mosques and police ahead of Friday prayers amid fears that far-right groups may try to confront worshippers.

Hours after the murder, the English Defence League held a demonstration in Woolwich, during which supporters, some wearing balaclavas printed with "EDL", engaged in running battles with police for almost an hour. They have since announced another gathering, to be held outside Downing Street on Monday, ostensibly to show support for British troops.

The league's Twitter account went into overdrive and thousands of people "liked" its Facebook page after the killing, although some people posting were challenging its ideology and ridiculing its beliefs. The BNP announced its own demonstration in Woolwich on 1 June.

The Met assistant commander, Mark Rowley, revealed that officers were monitoring social media for signs of people trying to exploit the attack to foment trouble. "Anybody seeing this as an opportunity to protest, cause mischief, or create tension is unhelpful and unwelcome, and we'd rather it did not happen," he said.

David Cameron and the London mayor, Boris Johnson, said the beliefs of the suspected attackers were alien to Islam.

"This was not just an attack on Britain and on the British way of life; it was also a betrayal of Islam and of the Muslim communities who give so much to our country," the prime minister said. "There is nothing in Islam that justifies this truly dreadful act." Johnson said it was "completely wrong to blame this killing on the religion of Islam".

Dr Matthew Feldman, co-director of the soon to be launched Centre for Fascist, Anti-Fascist and Post-Fascist studies at Teesside University, said extremist Muslims and groups such as the EDL "need each other". He said he feared they could engage in tit-for-tat attacks, with each side justifying its existence in terms of the other.

"We need to call out people who use this violence to advance what are clearly prejudicial agendas," he said.