Criminal justice think tank Crest Advisory says its research shows the “narrative” the scheme is a “toxic brand” is “fundamentally flawed”.
UK Muslims would be more likely to tip off the scheme when someone was being radicalised than the wider public.
But the Muslim Council of Britain said Prevent still needed to be overhauled.
The research was funded by a charitable trust with an interest in policing and crime reduction which for security reasons does not wish to be identified.
The survey showed that many of those questioned had not heard of Prevent before – amounting to 55% of Muslims and 68% of the general population.
But when offered “a neutral explanation” of Prevent, 80% of British Muslims and 85% of the wider public offered broad support for it, Crest Advisory says.
Some 67% of British Muslims surveyed said they would tip off the authorities about someone being radicalised, compared with 63% of the wider public.
The survey also found:
63% of Muslims and 67% of the wider public worried about Islamist extremism;
64% of Muslims and 71% of the wider public said they trusted the police.
“Our findings appear to fly in the face of a number of narratives commonly applied to British Muslims by some politicians, campaign groups and commentators about extremism and efforts to counter it,” said report author and Crest Advisory director Jon Clements.
“British Muslims are, broadly speaking, no more ‘in denial’ about Islamist extremism and the threat it presents than the population as a whole.
“Equally it is evident that British Muslims appear to be just as willing to step up and report concerns about an individual at risk of being radicalised as everybody else.”
epresentative samples of British Muslims and the wider public were interviewed by from Savanta Comres in October and November last year. Researchers also held focus group discussions in London, Slough, Watford, Bradford, Birmingham, Oldham, Cardiff and Glasgow.
Equalities campaigner Akeela Ahmed who advised the project said the research “underscores the urgent need to improve consultation with communities most affected by counter-terrorism and counter-extremism policies in general”.
She said the findings were “significant and provide a sound evidence base by which to bring fact and balance to a debate that has been raging for years.”
A Muslim Council of Britain spokesperson said the survey provided “valuable insight” and showed most people supported the “concept that prevention is better than cure”.
But they added that less than a third of the British Muslims surveyed who were actually familiar with Prevent were supportive of the scheme. They cited reasons including lack of trust and oversight and the MCB said this “demonstrate precisely why there needs to be an overhaul of the strategy” as “serious concerns” remained.