The Prince and Princess of Wales were questioned about the Duke of Sussex’s controversial autobiography as they opened a leading hospital – but one visitor told the future king to “keep going”.

Harry’s fraught relationship with William and Kate is laid bare in his memoir Spare which has become the fastest selling non fiction book in history, while a poll has found Harry’s popularity has dropped since its publication.

The couple, making their first official visit since the duke’s book was released on Tuesday, toured the new Royal Liverpool University Hospital in the home city of The Beatles and smiled, joked and posed for a large number of selfies with NHS staff they thanked for their efforts during the winter months.

When they arrived, William and Kate faced the first of a number of questions during their day visiting Merseyside, with a man in an outside area reserved for the media appearing to say, in the blustery conditions, “Do you ever plan to comment on Harry’s book sir?”

They ignored the question and, after being welcomed by senior figures from the hospital, began their tour of the critical care ward, meeting nurses and other staff looking after seriously ill patients.

At the end of the visit they met hospital volunteers in the building’s atrium and went on an extensive walkabout, shaking hands, praising staff and posing for selfies with the excited NHS workers.

One elderly woman, who had an appointment at the hospital, stood against a barrier waiting to talk to the future King and when he stopped she grasped his hand.

The 81-year-old, who only gave her first name Sylvia, said “Keep going Will, scousers love you”, and he replied, “I will do”.

Hospital staff member Nikki Langley, who works in administration, was left overjoyed when a smiling William posed for a selfie with her and three colleagues, the five all crowding into the image.

A few minutes later she asked Kate for a picture and the princess joked “I’m going to be told off by William” before posing with Ms Langley, who said afterwards: “It was a nice surprise, a very nice surprise. I wasn’t surprised they stopped for a selfie.”

Harry’s controversial autobiography includes claims his brother William physically attacked the duke and teased him about his panic attacks, and that the King put his own interests above Harry’s and was jealous of the Duchess of Sussex and the Princess of Wales.

Reports of a fractious friendship between Meghan and Kate were confirmed in Spare, with Harry recounting how the princess, pregnant at the time with Prince Louis, said she was owed an apology from his wife who had previously commented Kate was suffering from “baby brain” due to her “hormones”.

He shed further light on the row over Princess Charlotte’s bridesmaid dress claiming, contrary to reports at the time, Kate was not in tears but the incident had left Meghan “sobbing on the floor”.

During a series of interviews to promote Spare, Harry defended himself against strong criticism, following his revelation in the book he killed 25 Taliban members during the Afghanistan war.

He denied boasting about the killings, when interviewed by Stephen Colbert on CBS’s The Late Show, and claimed members of his family are in an active campaign to “undermine” his autobiography.

Later when William and Kate visited the Open Door Charity in nearby Birkenhead, an organisation supporting the mental health of young adults across Merseyside using culture and creativity, they ignored a Harry related question shouted by the media as they arrived.

After the visit, a broadcaster asked William: “Your Royal Highness, have you had a chance to read your brother’s book?” as the couple walked to their chauffeur-driven car but the prince did not acknowledge the question.

The King also carried his first official engagement since the publication of his son’s book, visiting the community of Aboyne, close to the late Queen’s Balmoral estate in Aberdeenshire, to tour the Aboyne and Mid Deeside Community Shed and meet local hardship support groups.

A YouGov poll has found the popularity of Harry has fallen since his book was published with 68% of 1,691 adults, polled on Tuesday and Wednesday, having a negative opinion about him while 24% thought positively.

The online research data group said the figures meant the duke had his lowest ever net favourability rating of minus 44, down from minus 38 last week, which had been his previous record low.