They aren't out of the woods yet, but for the first time in more than 24 hours Prince William finally felt able to offer a smile.

Leaving his pregnant wife's bedside last night after a six-hour vigil, the exhausted father-to-be fleetingly acknowledged the nation's good wishes before stepping into his car. Kate, the Duchess of Cambridge, was said to be feeling better but will continue to receive treatment for the next few days.

The Duchess, 30, has been on a drip in hospital after being admitted on Monday with an acute - and potentially dangerous - form of morning sickness.

St James's Palace said: "The Duchess of Cambridge is continuing to feel better. She and the duke are immensely grateful for the good wishes they have received.


"She will remain in hospital at present and will continue to be treated for hyperemesis gravidarum."

In spite of William's obvious concern, the couple may be forced to spend the first months of Kate's pregnancy apart if her medical condition does not improve, the Daily Mail understands.

The condition that the Duchess, who is believed to be only eight weeks pregnant, has been diagnosed with can last for the first five months of pregnancy - sometimes even for the entire duration.

It may require regular hospital treatment because it can lead to severe dehydration, putting mother and baby at risk.

This means that Kate, who is being attended at the King Edward VII Hospital in London by not just one but two of the Queen's personal doctors as well as the hospital's own medical staff, may be forced to remain in the capital for the foreseeable future instead of returning to their rented farmhouse on Anglesey in North Wales, close to RAF Valley, the base where William is a Search and Rescue helicopter pilot.

However sources close to the couple say the Prince is duty bound to spend the first half of next year at RAF Valley in order to keep up his flying hours, leaving him with a potentially agonising dilemma.

Such enforced separation is far from ideal, and clearly William and Kate will do anything they can to avoid it, but the pair may have little choice because William needs to seriously "bump up" his flying hours after scraping through with the bare minimum this year because of his Diamond Jubilee commitments, sources have revealed.

"With their Pacific tour and all the extra engagements both he and Catherine have had, the duke was able to meet only the minimum commitments required in terms of flying hours and shifts this year," an aide explained.


"Some time ago the duke made clear to his office that he would be carrying out fewer public engagements in the first half of 2013 in order to fully commit to his job.

"He even instructed that when he was required to work, the engagements needed to be clustered together in order to minimise the time he was spending travelling to and from Wales.

"He is very passionate about his job and is part of a team. He doesn't want to - and can't - let anyone down."

Just where this leaves their diary is still a matter of debate. Staff had expected the Duchess to take on more public engagements and patronages in order to make up the shortfall.

Now, an aide says: "No one knows what is going to happen for sure. Everything is up in the air."

For now, however, William has been given compassionate leave from his job to remain in London to be with his wife.

Dressed casually in a sweatshirt, chinos and trainers, the second in line to the throne arrived at the hospital yesterday with his police protection officer at 11.30am and left just after 5.45pm.

A source told the Mail that while the Duke was encouraged by his wife's condition, he remained extremely concerned because it was "such early days".

"There's a very good reason that pregnancies aren't normally made public until after a successful 12-week scan, so the couple obviously remain concerned," they said.

The Duchess received no other visitors, even though her sister Pippa was seen walking through a shopping area only a few minutes' drive away.

Her parents, Michael and Carole Middleton, have released no official statement.

They were pictured driving to and from their Georgian manor house in Bucklebury, Berkshire, several times during the day.

The Queen, William's grandmother, continued with a planned investiture ceremony at Buckingham Palace yesterday.

Although she has declared herself "delighted", the Queen clearly isn't taking any chances either and Kate is currently being attended by both her personal surgeon/gynaecologist, Alan Farthing, and his predecessor.

Mr Farthing, former fiance of murdered television presenter Jill Dando, was appointed in 2008 and this will be his first royal birth.

His predecessor Marcus Setchell held the role for 18 years and delivered both the Countess of Wessex's children as well as leading her medical care when she had an ectopic pregnancy.

Historically the Royal Family aren't known for their bedside manner - not a single member of the family visited the elderly Prince Philip when he was in hospital in Scotland with a bladder infection this summer.

William drove with his wife of 18 months to hospital on Monday and stayed at her bedside until early evening.

He is expected to return again today and every day until Kate is released, which may not be until the end of the week.

Although Kate has cancelled her three planned engagements this week, William is expected to meet his own two public commitments this weekend - an appearance at a charity tennis gala on Saturday and a visit to the British Military Tournament on Sunday - although the palace has yet to confirm this.