The survey was conducted by the ICM polling institute for a Channel 4 documentary airing on Wednesday entitled "What British Muslims Really Think" and presented by anti-racism campaigner Trevor Phillips.
Out of the 1,081 respondents, 52 percent said they believed homosexuality should be illegal, compared to 22 percent of all Britons.
Thirty-nine percent believed women should always obey their husbands and 23 percent said Islamic sharia law should apply in areas with high Muslim populations.
Phillips said the survey showed Muslim integration would be "the hardest task we've ever faced".
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"It will mean abandoning the milk-and-water multiculturalism still so beloved of many, and adopting a far more muscular approach to integration," he added.
The poll has already stirred controversy, with many campaigners objecting to the singling out of Muslims.
"Discussions and proposals to promote integration and cohesion are always welcome," Miqdaad Versi, assistant secretary general of the Muslim Council of Britain, wrote in the Guardian newspaper on Tuesday.
Varsi pointed to the poll's finding that 86 percent of respondents said they were very attached to Britain and 78 percent said they wanted to integrate.