This compares with 24 per cent who think the prince should not stand aside for the duke, while 29 per cent do not have strong feelings on the issue.
But the survey also suggests that 48 per cent of people in the UK still believe Charles will do a good job, compared with 19 per cent who think he will do a bad job and 27 per cent who think he will do neither.
The survey of 2,055 British adults on March 24 and 25 also found that the proportion of people who view Charles favourably has increased since 2018 to 43 per cent – up 11 percentage points.
More than a third (36 per cent) feel the same for Camilla, the Duchess of Cornwall.
Yet opinion of Charles is higher than the Duke and Duchess of Sussex, Prince Harry and Meghan, whose popularity has worsened in the past four years.
Meanwhile, 69 per cent now have an unfavourable opinion of Prince Andrew, the Duke of York.
The research also looked at where Britons stand on abolishing the monarchy.
More than four in 10 people (44 per cent) think abolishing the monarchy would be worse for Britain, compared with 22 per cent who think it would be better.
“At the moment only a minority of people believe Britain would be better off without the monarchy, and the popularity of the Queen and the Duke and Duchess of Cambridge remains strong," said Gideon Skinner, head of political research at Ipsos.
“Looking to the future, half of Britons have faith in Prince Charles as a future king and more people view him in a positive light than four years ago.
“However, with the popularity of Prince William not far behind that of the Queen, Britons also wonder whether Prince Charles should step aside in favour of his eldest son.
“But their actions now are still important for the longer-term future of the royal family.”