More than half of the 1,000 questioned favoured William taken the throne, even though his father is ahead of him in the pecking order.
William's girlfriend, Kate Middleton, is also popular with Britons, with 72 per cent saying she would make a good addition to the royal family.
However, Charles' second wife, Camilla, the Duchess of Cornwall, didn't fare so well.
Just 42 per cent regard her as a good ambassador for the royal family and 68 per cent said they preferred the prince's first wife, the late Princess Diana.
Former royal correspondent Jennie Bond said: 'Prince Charles does seem to have a real image problem.
'Even though he is undoubtedly the best-trained heir to the throne we've ever had, the public seem reluctant to accept him as king.
'The damage to his image caused by the break-down of his marriage to Diana seems irreparable.
'I think it's sad; we should be more forgiving as a nation and accept that Charles is a far wiser head on more experienced shoulders than a boy of 25 who still has much to learn and do.' Overall, three-quarters of Britons said they were in favour of retaining the monarchy, but the same percentage question whether it delivers value for money and want it to use less of taxpayers' money.