Britain’s Muslim communities have “separatist” tendencies and a “deeply worrying” belief in conspiracy theories, according to one of the government’s favourite centre-right thinktanks.

The controversial Policy Exchange report however does acknowledge that 93% of British Muslims have a strong attachment to Britain and their attitudes to many issues such as the NHS, unemployment and immigration are broadly in line with the rest of the population.

The report published on Friday comes out before the findings of a government-commissioned review, chaired by Dame Louise Casey, into integration and community cohesion in Britain are due to be published early next week.

The Muslim Council of Britain (MCB) strongly criticised the thinktank’s report, saying it seemed to pursue an agenda to cast British Muslims as separate, dangerous and in need of saving, while the thinktank had “provided ample fodder to countless headlines demonising Muslims”.

The findings of the Policy Exchange report, Unsettled Belonging, are based upon an ICM poll which is described as the most comprehensive to date of British Muslim opinion based on interviews with 3,000 people.

Its findings say that Britain’s Muslims “live on average somewhat more separately than other significant minorities” but 53% show an appetite to integrate more with non-Muslims in all aspects of life.

However it also found that 31% believed the US government was behind the 9/11 terror attacks with a further 7% blaming the Jews and only 4% saying al-Qaida was responsible.

The thinktank also highlighted findings that British Muslims were more likely to condemn acts of political violence and terrorism than the rest of the population but that one in four British Muslims claimed that “extremist views do not exist”.

When asked what they would do if they became aware someone close to them was “getting involved with people who support terrorism in Syria” only 52% said they would report them to the police.

A foreword to the pamphlet by the Labour MP for Birmingham Perry Barr, Khalid Mahmood, said it was startling that so many British Muslims seemed ready to entertain wild and outlandish conspiracy theories about “dark forces” at work to “do down Muslims”.

He said that the poll found that organisations such as the MCB had very little support among British Muslims and were failing to reflect their views on issues such as Prevent. He suggested that the government needed to realise their views only represented “the sectional demands of those on the fringes of British Muslim life”.

David Goodhart, co-author of the report and head of the thinktank’s integration and immigration unit, said: “British Muslims as a whole continue to live somewhat more separately than other large ethno-cultural minorities – in neighbourhoods and schools, in terms of women not working, and in terms of attitudes and religiosity.

“However, the promising news from this survey is that when it comes to everyday life, British Muslims, and their concerns and interests, are increasingly part of the mainstream, and to a much greater extent than one would assume listening to many of the organisations that claim to speak for Muslims.”

The MCB responded by saying Policy Exchange had misused otherwise promising ICM poll results in its “decade-long” attempt to “delegitimise” its organisation.

“There are some disturbing results in the poll that deserve further investigation. A large minority of Muslims seem to agree that conspiracy theories ‘often contain elements of truth’, in line with the broader UK population (40% v 37%). In addition, more British Muslims have conspiracy views about 9/11 in a proportion that is high and similar to results polling the US population on this issue,” said an MCB statement.

“As the Muslim Council of Britain, we will be meeting to discuss how to understand this problem properly so that action can be taken to challenge these worrying views.”