Attitudes towards many issues, such as the NHS, unemployment and immigration, are broadly in line with the rest of the population, according to the Policy Exchange study.
But 31% of Muslims thought the United States government was behind the 9/11 terror attacks and 7% blamed Jews while just 4% believed al Qaeda was responsible, the think-tank said.
It found that 26% of Muslims did not believe in extremism and 48% would not turn to the police if someone close to them became involved with people linked to Syrian terrorism, the research revealed.
Labour’s Khalid Mahmood said the findings made clear that British Muslims were no different in their views in many areas to the rest of the population but raised concerns over the significant numbers who doubted the existence of extremism.
In a foreword to the report, the shadow Europe minister said: “Even more startling is the fact that so many British Muslims seem ready to entertain wild and outlandish conspiracy theories about the way the world works, believing that dark forces are at work to ‘do us down’ as Muslims.
“From the attacks of 9/11, down to the more recent conflict in Syria, too many people seem ready to believe that these events are being deliberately organised and manipulated - whether by the American Government, Jews, or some other force - with the express intention of damaging Muslims.
“Of course, there is no denying that for many British Muslims, problems of racism, harassment and Islamophobia are a serious cause of worry. But it is deeply troubling that this seems to have led a not-insignificant minority to believe that the world is at the mercy of the machinations of dark, anti-Muslim forces.
“This readiness to believe in conspiracy theories and the mentality of victimhood to which it speaks is having a pernicious effect on British Muslims and the way they see the world. It is holding us back - as a community - and ensuring that we remain locked in a paranoid and at times fearful world view.”
The report, Unsettled Belonging: Britain’s Muslim Communities, is based on research carried out by polling company ICM with more than 3,000 people.
It found 93% of respondents had a fairly strong or very strong attachment to Britain and more than half wanted to fully integrate with non-Muslims in all aspects of life.
More Muslims condemned terrorism than the rest of the population - 90% to 84% - and 55% wanted to see extra police on the streets.
But 43% supported the introduction of Sharia law and 1% said they favoured fully separate Islamic areas in Britain.
Martyn Frampton, head of security and counter extremism at Policy Exchange, said: “In nearly every walk of life, British Muslims are no different in their views and priorities to their non-Muslim neighbours.
“They believe the NHS, jobs and immigration to be the most pressing issues facing the country and worry deeply about the effect of drugs and drinking on their communities.
“However, the research found a deeply worrying belief in conspiracy theories such as 9/11. Unlike the general population, nearly a third of British Muslims believe the American government was responsible for the attacks on the Twin Towers, while a surprisingly tiny number attributed blame to al Qaeda.”
The report found that the Muslim Council of Britain enjoys little support in the community, with just 9% of respondents backing it.
It also suggested the Government should not be “spooked” into abandoning or apologising for its controversial Prevent agenda, which tries to stop people being drawn into terrorism, because Muslim communities are “generally relaxed” about intervention to tackle extremism.
David Goodhart, head of Policy Exchange’s demography, 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.”