Of 1,000 people questioned, 70% doubted the account, according to the British Market Research Bureau.
Almost a quarter of people who described themselves as Christians shared their scepticism.
St Helen's Church in Bishopsgate, London, which commissioned the survey, has produced a film of "sound evidence" supporting the Bible's account.

More than a fifth of Christians who answered said they did not believe Jesus was both God and Man - another central tenet of Christianity.
Young people were particularly sceptical.
BBC religious affairs correspondent Robert Piggott said the findings suggested a fading influence for the Church's teaching in a secular age.
Nostalgia
"They also reinforce evidence that believers are increasingly willing to pick and choose which elements of the Bible's story they accept," he added.