The YouGov survey for the Sunday Times found 58% support for Charles to relinquish his claim to the throne in favour of his son, against 25% who say he should not.
By a majority of 60% to 21% - almost three to one - participants in the poll said they expected William to make a better king than Charles, with women particularly favouring the young prince by a margin of 68% to 18%.
But a separate Mori poll for The Observer and Sunday Mirror found 40% support for Charles being the next monarch, against 42% for William.
Only 16% of people polled by YouGov think Camilla should one day be Queen. Just 24% believe she will eventually be Queen. Clarence House has said that she will describe herself as Princess Consort if Charles accedes to the throne, but it is thought legislation would be required to prevent her officially taking on the title of Queen.