The Princess of Wales has taken another step on her road to recovery from cancer by enjoying a ski holiday over the New Year.

The Mail on Sunday can reveal that Kate – along with Prince William and their children Prince George, Princess Charlotte and Prince Louis – enjoyed a quiet break in the Alps just over two weeks ago.

They are said to have slipped away from their home at Anmer on the Sandringham estate shortly after Christmas, and spent several days away, along with members of the Middleton family.

The couple and their children were spotted enjoying morning hot drinks at a mountaintop restaurant that is a popular stop-off point for British skiers and has panoramic views of snow-covered peaks.

It is believed they returned for a meal at the same restaurant, which was once a shepherd's hut.

A member of staff revealed: 'It was lovely to see Kate relaxing and enjoying herself.

'They looked like a normal English family, and a lot of people didn't recognise them. It was not the first time we had seen them. They have been coming here for years. I think they love the area. We often see Kate's sister Pippa as well.'

Although the trip will be viewed as a positive sign in Kate's ongoing recovery from cancer, Kensington Palace have stressed that the princess's return to full duties will only be gradual.

The restaurant has indoor and outdoor areas, and is known for its cosy atmosphere and fine food, with an open fireplace for skiers to warm themselves before heading back on to the piste.

It stands at an altitude of more than 6,000ft, and can be accessed only by skiers who go down a red run, although visitors on foot who book a table can get a ride up the mountain to reach it in the restaurant's tracked snow taxi.

The suggestion that George, 11, Charlotte, nine, and Louis, six, arrived on skis suggests that they are already competent on the slopes.

Kate – who, after a visit to the hospital where she had chemotherapy, announced last week that she was 'in remission' from cancer – spent time with her brother James while on her break, including seeing him at the restaurant.

An onlooker said: 'James was there with his wife and then Kate arrived with Charlotte and Louis. It seemed like a bit of a Middleton family knees-up. Everyone seemed to be really happy.

'There were no airs and graces and actually they seemed like any normal family enjoying a ski break. There were lots of laughs and the children were very polite.

'The only reason you would have known that they were people of importance was because when Kate arrived so did a group of security guards. Kate looked like she was having a lovely time.'

James, 37, shared a set of pictures on Instagram earlier this month showing himself, his wife Alizee, their one-year-old son Inigo and two of their dogs, with a background of snowy mountains on an apparent ski trip. 

In a post accompanying the pictures, he opened up about his battles with depression, saying: 'The January blues used to hit me hard… and to some extent it still does.'

But he also revealed: 'We started the New Year with an adventure into the mountains. We were lucky enough to be engulfed by blue skies and cold crisp air.'

Kate is thought to have returned back to the UK in time to celebrate her 43rd birthday at home on January 9. She then undertook her first solo engagement in more than a year at the Royal Marsden Hospital in London, where she was treated for her cancer.

Her visit to the hospital was described by royal watchers as part of her 'carefully calibrated plan to manage her recovery and measured return to official duties'.

A spokesman for Kensington Palace declined to comment.