The King made a triumphant return to public duties last week following his cancer diagnosis.
He will soon embark on a packed summer schedule to include garden parties, the Chelsea Flower Show, Trooping the Colour and a trip to Normandy to commemorate the 80th anniversary of the D-Day landings alongside his son, the Prince of Wales.
A palace source said: “While, as ever, their commitment to service is not driven by the ups and downs of polling, I know both Their Majesties have been buoyed and encouraged by the warmth and support they have received from the public in the past challenging months, of which this is further evidence.”
The Duchess of Sussex was the only member of the royal family whose approval ratings did not rise, unchanged at 25 per cent.
The Princess of Wales enjoyed the largest bounce, with a jump of 10 per cent taking her to 69 per cent.
The boost saw her join her husband, Prince William, to secure a joint place at the top of the table.
The princess has endured a difficult few months after being admitted to hospital in January for major abdominal surgery, only to discover that she had cancer.
The mother-of-three has since embarked on a course of chemotherapy treatment and has withdrawn from the public eye as she focuses on her recovery.
The Prince of Wales, who recently returned to work after a three-week Easter break with his family, has seen his own popularity jump eight percentage points to 69 per cent after putting his public duties aside to care for his wife.
Just behind the Waleses is the Princess Royal, on 64 per cent, marking a jump of five points, with the King at 56 per cent with a jump of four points and the Queen at 45 per cent, up from 40.
Even the Duke of Sussex, who these days languishes at the bottom of such tables alongside his wife, Meghan, and uncle, the Duke of York, enjoyed a jump of four percentage points on last year, taking him to 31 per cent.
Prince Andrew, who was seen leading his family at a memorial service for King Constantine of Greece in February and also joined senior royals at church on Easter Sunday, enjoyed a jump of one percentage point, taking him to 12 per cent.
The poll of 2116 adults was conducted by Ipsos for the Mail on Sunday.
Gideon Skinner from the polling firm, told the newspaper: “As the King returns to public duties he is greeted by a further boost in favourability ratings for himself and other core members of the Royal family.
“The question for the monarchy is whether this is a short-term improvement driven by a swell in public sympathy or whether it can be maintained – particularly among younger generations where the royals need to focus their engagement effort.”
The results do reflect the age divide when it comes to opinions about the royal family, with one-third of young people saying it “would be better” if the monarchy was abolished, compared with just one in six older people.
Conservative voters are the most supportive, but the King enjoys particularly strong backing across the political spectrum.
Of all those polled, 73 per cent of Conservative voters, 68 per cent of Liberal Democrats, and 49 per cent of Labour voters agreed that he has done “very” or “fairly” well.