The Princess of Wales has reportedly been spotted out and about in public, looking “happy, relaxed and healthy”.

London’s The Sun newspaper reported Kate spent Saturday morning watching her children – Prince George, 10, Princess Charlotte, eight, and Prince Louis, five – playing sport near the Wales’ Windsor home.

She was also seen on the same day with husband Prince William at a busy farm shop on the Windsor Castle estate.

A witness at the farm shop told The Sun she was pleasantly surprised to see the princess of Wales out in public and looking well.

“After all the rumours that had been going round, I was stunned to see them there,” they said.

“Kate was out shopping with William and she looked happy and she looked well.”

“The kids weren’t with them but it’s such a good sign she was healthy enough to pop down to the shops.”

No photos have yet emerged of either outing.

Tweet from @TheSun

If confirmed, the weekend’s sightings would be among the first of Kate since Kensington Palace announced in mid-January she would take months out of the spotlight to recuperate after planned abdominal surgery.

It came amid reports in Britain at the weekend that the princess might soon give more details about her mysterious health emergency.

Two weeks ago Kate was photographed in a car being driven by her mother Carole Middleton. Last week she was seen, briefly, sharing a car with husband Prince William on their way to London.

It follows an extraordinary storm after last week’s release of a photo of Kate and her three children to mark Mother’s Day in Britain.

Concerns about digital manipulation were quickly raised and international picture agencies issued “kill” notices for the photo – which Kensington Palace said had been taken by Prince William. Instagram has also placed a warning note on the photo.

Kate took the blame in a rare public statement apologising for the “confusion” caused by her editing.

“Like many amateur photographers, I do occasionally experiment with editing,” she wrote on social media.

“I wanted to express my apologies for any confusion the family photograph we shared yesterday caused.”

The palace has faced growing pressure over the debacle with the controversy branded as damaging to the public’s trust in the royal family. But, apart from Kate’s statement, it has remained silent.

Kate had surgery at the London Clinic on January 16 and has long been expected to return to royal duties after Easter. At the time, the palace said only that her condition was not cancerous, and that she wanted her personal medical details to remain private.

The Windsor Farm Shop is a popular destination on the royal estate. Photo: windsorgreatpark.co.uk

However, The Sunday Times has reported that those close to Kate and William said the couple will disclose more information about her recovery in due course.

“They are at their most open when out interacting with members of the public and I can see a world in which the princess might discuss her recovery out on engagements. If she was going to do it, that’s how she would do it,” a source told the paper.

A friend reportedly said: “They will want to be clear and more open, but they’ll do it when they feel ready. I would expect that to be her instinct and it will be her call. They’re not going to be rushed.”

The newspaper also said Kate was likely to resume royal duties after her children’s Easter school holidays. They are due back at school on April 17.

Prince William will also take time away from public duties for the Easter break.

The Sunday Times also reported that the Waleses intend to continue releasing photographs marking their children’s birthdays. Prince Louis turns six on April 23 and a photo is expected – although there has reportedly been no “firm decision” on if it will be taken by Kate.

Kensington Palace declined to comment.