British Muslims are more likely to feel a stronger connection to Britain than the population at large, according to polling, which also found that more than half think that homosexuality should be illegal.

Extensive polling conducted by ICM suggests that in most cases attitudes held by the British Muslim population do not broadly differ from those held by the population at large, but there are significant differences when it comes to some issues such as homosexuality and women’s rights.

Trevor Phillips, the former head of the Equality and Human Rights Commission, said the findings were “extremely worrying” as they suggested on many issues Muslims were “nation within a nation”.

He called for a more “muscular approach” to integration.

The research suggests that 86% of British Muslims feel a strong sense of belonging in Britain, which is higher than the national average of 83%. A large majority (91%) of the British Muslims who took part in the survey said they felt a strong sense of belonging in their local area, which is higher than the national average of 76%.

Of those questioned, 88% said Britain was a good place for Muslims to live in, and 78% said they would like to integrate into British life on most things apart from Islamic schooling and some laws.

However, when asked to what extent they agreed or disagreed that homosexuality should be legal in Britain, 18% said they agreed and 52% said they disagreed, compared with 5% among the public at large who disagreed. Almost half (47%) said they did not agree that it was acceptable for a gay person to become a teacher, compared with 14% of the general population.

In a series of questions on the terror threat in Britain, 4% said they sympathised with people who took part in suicide bombings (1% said they completely sympathised and 3% said they sympathised to some extent), and 4% said they sympathised with people who committed terrorist actions as a form of political protest generally.

Nearly a quarter (23%) supported the introduction of sharia law in some areas of Britain, and 39% agreed that “wives should always obey their husbands”, compared with 5% of the country as a whole. Two-thirds (66%) said they completely condemned people who took part in stoning adulterers, and a further 13% condemned them to some extent. Nearly a third (31%) thought it was acceptable for a British Muslim man to have more than one wife, compared with 8% of the wider population.

ICM conducted face-to-face, at-home interviews with a representative sample of 1,000 Muslims across the UK between 25 April and 31 May 2015. A control sample of 1,008 people representative of the country as a whole were interviewed over the phone to provide a comparison.

The polling was commissioned by Channel 4 for a documentary, What British Muslims Really Think, which is due to be broadcast on Wednesday presented by Phillips.

Speaking on BBC Radio 4’s Today programme, he said: “On specific issues – families, sexuality, gender, attitudes towards Jews and on questions of violence and terrorism – the centre of gravity of British Muslim opinion is some distance away from the centre of gravity of everyone else’s opinion.

“One in six Muslims say they would like to live more separately, a quarter would like to live under sharia law. It means that as a society we have a group of people who basically do not want to participate in the way that other people [do].

“What we also found is that there is a correspondence between this desire to live separately and sympathy for terrorism. People who want to live separately are about twice as likely to say that they have sympathy for terrorist acts. Anybody, including most people in the Muslim community, would find that extremely worrying.”

Phillips said we should not be afraid of challenging Muslims on the core values of British society.

He said: “We are more nervous about Muslims because we feel people will be offended. But my view is that looking at the results of this survey, which have surprised me, that we have gone beyond the situation where we can say: ‘OK, don’t worry; they will come round in time,’ because that is not going to happen we have to make things change now.

Khalid Mahmood, Labour MP for Perry Barr, welcomed the fact that the polling had highlighted that the vast majority of Muslims had a strong attachment to Britain, but added: “I think the real issue is that their participation in British society needs to increase.”

“What this [polling] highlights is that the community hasn’t progressed from what was happening in the 80s and ... that they have been isolated without being able to have further integration,” he said. Mahmood argued that this was in large part due to a shortage of housing, which had led to overcrowding in British Asian areas. “It’s not for the want of trying,” he added.

Shaista Gohir, the chair of the Muslim Women’s Network UK, said interviews with other religious groups such as devout Jews and Christians would probably reveal similar social attitudes to those thrown up by the polling. She said that although any prejudice against gay people was unacceptable, the fact that nearly 50% of Muslims did not think homosexuality should be illegal was a sign that attitudes were shifting.

“Although they may not accept it from a religious point of view, [Muslims] accept that people should be able to have the freedom and right not be discriminated against and and live their lives,” said Gohir, adding that LGBT Muslims were beginning to speak out publicly and increasing numbers of Muslim families were having to come to terms with family members coming out as gay.

She said the findings on women’s issues did not reflect changing attitudes among younger generations of British Muslims, arguing that younger Muslim women were coming to better understand what their rights were according to the teachings of Islam.

Gohir said the findings went against the portrayal in the media of Muslims not feeling proud to be British. “These stereotypes do not reflect the reality of Muslims in Britain,” she said. “It is important to also display these positive attitudes … because that represents the British Muslim majority.”