Among 18 to 24-year-olds, only 30% say the monarchy is "good for Britain", compared with 77% among the over-65s.
The survey of more than 2,000 adults in Britain comes as the first anniversary approaches of the death of Queen Elizabeth II.
The pollsters found that overall, 62% want to keep the monarchy.
But they report a "remarkable difference between generations", with younger people much less supportive on remaining a monarchy and more sceptical about the Royal Family representing good value for money.
For King Charles, as he approaches his first year on the throne, 59% of people thought he was "personally doing a good job".
The pollsters say there has been a broadly consistent picture of "overall positivity towards the monarchy", but there is also a sizeable and rising minority who are opposed.