Prince William's pregnant wife Catherine said she was feeling much better as she was discharged from a London hospital on Thursday following four days of treatment for acute morning sickness.

Holding a bouquet of yellow roses and wrapped up in a dark coat and blue scarf to protect against the cold, the former Kate Middleton smiled as she left the private King Edward VII Hospital with her husband.

The Duchess of Cambridge, 30, mouthed "much better" and nodded when she was asked by the waiting international media if her condition had improved, before the couple were driven away by a security team.

Kate will now have a "period of rest" at Kensington Palace in central London where the couple have an apartment, said a statement from their office at St James's Palace.

"Their Royal Highnesses would like to thank the staff at the hospital for the care and treatment The Duchess has received," the statement said.

Her departure from the hospital comes a day after it apologised because a nurse unwittingly released Kate's private medical details to hoax callers from an Australian radio station.

Kate was admitted to hospital on Monday with hyperemesis gravidarum, a severe form of morning sickness that affects about one in 200 pregnant women and is sometimes associated with twins.

The pregnancy, which was only announced after she went to hospital, is believed to have not yet reached the 12th week. It will be the first child for the couple who married in April 2011.

The baby will be third in line to the British throne, now occupied by Queen Elizabeth II, following last year's historic agreement among Commonwealth realms to end the practice of male primogeniture.

William's father Prince Charles, the heir to the throne, said he was "thrilled" by news of the pregnancy.
"It's a very nice thought to become a grandfather in my old age, if I can say so," Charles, 64, told reporters. "I'm very glad my daughter-in-law is getting better, thank goodness."

He also joked when he first spoke to reporters: "How do you know I'm not a radio station?"

Sydney's 2Day FM station said sorry after two presenters posing as the queen and Prince Charles got through despite their poor imitations of English accents.

Hospital chief executive John Lofthouse said it was considering legal action.

"I've received advice that what the Australian broadcasters did may well have broken the law," he said. "On the other hand they've apologised for it so we're going to have a long and careful think about what, if anything, we do."

In the recording of the hoax call, the nurse can be heard saying about the duchess: "She hasn't had any retching with me since I've been on duty and she has been sleeping on and off."

The Australian station was milking the publicity Thursday by boasting of the "biggest royal prank ever", despite an earlier apology by presenters Mel Greig and Michael Christian.

"We were very surprised that our call was put through. We thought we'd be hung up on as soon as they heard our terrible accents," the presenters said in a statement.

The hospital has also treated the queen, her husband Prince Philip and Charles' wife Camilla over the years. The queen is its patron.

William, second in line to the throne after Charles, visited Kate in hospital every day, spending hours at her bedside. Kate's younger siblings Pippa and James also paid her a visit on Wednesday.

William's own plans as his wife recovers are uncertain. The Royal Air Force search and rescue helicopter pilot is reportedly due back at his base in Wales next week but it is possible he may decide to stay in London.

He is due to attend a charity gala in London on Saturday, while Kate has cancelled all engagements for the coming days although there were reports she would attend a screening of "The Hobbit" next week.

Speculation about her pregnancy has been intense ever since the couple married in a globally televised event in London's Westminster Abbey on April 29, 2011.