The Ipsos poll released on Friday found 49 percent of the public believed Charles, who will be formally crowned on 6 May, was doing a good job versus 9 percent thinking otherwise.
Almost a third had no view either way.
The approval level is down from 61 percent last September after he succeeded his mother Queen Elizabeth.
"With less than two weeks until the coronation, King Charles may be happy to know that half of Britons think he is already doing a good job, numbers recent prime ministers would envy," said Kelly Beaver, chief executive of Ipsos UK and Ireland.
"It's a good start for Britain's new King and something he will no doubt want to continue to work on once the coronation quiches are eaten and the bunting is down."
A separate Ipsos survey also found 57 percent were satisfied with how Charles was doing his job, down 8 percentage points from when a similar poll was carried out in May last year.
When it came to which royal the public liked best, Kate, the Princess of Wales, came out on top ahead of her husband and heir to the throne Prince William, "any of the king's grandchildren", and Charles's sister Princess Anne.
Among the least favourite members were Prince Harry and his wife Meghan, and the king's second wife Camilla, now the Queen Consort, the pollster said.
- Reuters
