It follows a call by the UK’s terror watchdog for an independent review of Prevent.
Bella Sankey, director of policy for human rights group Liberty, said the poll was a “damning indictment” of Prevent, which she branded “clumsy and offensive”.
She added: “The Government has had no qualms dismissing the valid concerns of human rights campaigners, teachers and religious groups, but the British public will prove harder to brush off.”
Shadow home secretary Andy Burnham said the Government’s approach was “clumsy at best and highly divisive at worst”.
He added: “This is the biggest challenge of our times but this poll shows that the Prime Minister is failing to rise to it.”
He said Prevent “needs a wholesale rethink”.