Three quarters of people believe that the newborn son of Prince William and Kate Middleton will one day accede to the throne to which he is third in line, the ComRes survey for The Sunday Telegraph found.
Just 9 per cent of those questioned think that he will not become king because Britain will have become a republic, whereas a poll in 2011 found that a quarter of people expected a republic to emerge within 50 years.
The poll suggests that the majority of the country sees no benefit in republicanism, with some two thirds of those polled (66 per cent) thinking that Britain is better off as a monarchy.
Only 17 per cent wanted a republic instead.
More From This Section
The survey also highlights the rising popularity of the Duke and Duchess of Cambridge, particularly among the young.
They, along with Prince Harry, are the three most popular members of the Royal family behind the Queen.
More than half (53 per cent) of those questioned today think that Britain would be worse off without the Royal family while only 14 per cent believe the British would be better off without them.
The poll suggests that republicans doubt that the abolition of the monarchy will happen this century.
Prince George's reign - which would follow those of the Prince Charles and Prince William - is unlikely to begin for another half century and could last into the 22nd century.
The figure suggests that the future of a monarchy built on popular support has been ensured and shows a far lower level of expectation that there could be a republic than previous polls.