A YouGov study carried out by anti-racism charity Hope Not Hate found that just 8% of the party's members "would be proud of Britain if we were to elect a Muslim as our Prime Minister".
But 43% agreed that they "would prefer to not have the country led by a Muslim".
The findings come after Home Secretary Sajid Javid forced the Conservative leadership contenders to agree to an independent probe into allegations of anti-Muslim prejudice in the party.
The survey also revealed that 67% of Tory members believe that “there are areas in Britain that operate under Sharia law", with just 18% disagreeing with that statement.
Meanwhile 45% said there were "areas in Britain in which non-Muslims are not able to enter" - with just over a third (34%) saying they did not believe that to be the case.
Forty percent of those surveyed said Britain should lower the number of Muslims entering the country, compared to just five percent who said the same for Christians or Jewish people. [PoliticsHome] Read more