Queen Camilla said the royal was doing “very well” with his cancer treatment, in a speech at the official opening of a new £50 million cancer treatment facility.

The Queen unveiled a commemorative plaque and met staff and patients at the new Dyson Cancer Centre at the Royal United Hospital in Bath.

In a speech, she said: “There is a very welcoming atmosphere and you can see that it actually lifts people’s spirits in very difficult times.”

The new centre has facilities for oncology, chemotherapy, radiotherapy and a 22-bed ward as well as research laboratories.

Suzie Moon, from the charity Macmillan, which runs a wellness centre at the new centre, asked the Queen about the King. She replied: “Yes, he is very well.”

King Charles III is being treated for an unspecified type of cancer and public appearances were postponed in February before public events resumed in April.

The Princess of Wales has received chemotherapy after her cancer diagnosis.

Queen Camilla spoke to other cancer patients, including 55-year-old Paul Holdway from Trowbridge, Wiltshire, who was recovering from a stem cell transplant for blood cancer.

Mr Holdway told the Queen that he was tired after the treatment.

Camilla responded lightheartedly, apparently alluding to her husband’s cancer treatment: “Men don’t admit it,” Mrs Holdway said later.

The centre, which treats patients from Wiltshire and Somerset, can accommodate up to 300 people a day.

Nic Noble raised around £1 million for the new centre in memory of her sister, who died of cancer, and was present at the royal visit.

She said: “Fortunately, my mother was introduced to her (the Queen), which was a delight for me – she had a nice chat with her.”

She added that the Queen was “just such a wonderful woman. She was down to earth and put everyone at ease.”

Diane Young, Ms Noble’s mother, said she had spoken to the Queen about how “terrible” the facilities had been that had been replaced by the new centre.

“We talked about what a wonderful new centre this is and how proud I am of Nic and her late sister. She was very approachable and obviously impressed with the new centre,” she added.

During her visit, the Queen was presented with flowers by members of the public.

£40 million of the centre’s costs were covered by government funding and £4 million was donated by the James Dyson Foundation.

Sir James Dyson, founder and chief engineer, had previously stated that the hospital needed new premises and described the old cancer unit as “very old” and “not fit for purpose”.

The charity Macmillan Cancer Support donated £1.5 million and a further £1 million was donated by the Medlock Charitable Trust.

RUHX, the trust’s official charity, also raised £5 million for the centre, where the charity Macmillan has also opened a wellness centre.

After the hospital visit, Queen Camilla travelled to the village of Lacock in Wiltshire, where an egg manufacturer opened a new headquarters and egg packing facility.

Stonegate Farmers was founded in 1926 as a cooperative of farmers who brought their eggs to market.

They are now known throughout the country for the Clarence Court brand.