The Princess of Wales has reportedly been spotted smiling alongside her husband during a visit to a farm shop in Windsor.

Kate’s recovery from surgery appears to have progressed after footage obtained by The Sun showed her and William at the local business on Saturday.

In the video the princess can be seen with her hair down, wearing a black jacket and leggings, chatting with William and carrying a large white bag.

The Windsor Farm Shop is a short drive from their Adelaide Cottage home in the grounds of Windsor Castle.

People flock to the shop, which was the idea of the late Duke of Edinburgh, to buy locally sourced goods and produce from the royal estates.

Nelson Silva, who saw the royal couple, told TMZ: “I noticed a couple choosing loaves of bread and the woman turned her face and I felt like I had seen the face before. It was familiar.

“I went to my car and as they came out of the shop I just filmed them. I think they walked out through a gate out of the grounds. They just vanished and I didn’t see a car.

“Kate looked happy and relaxed. They look happy just to be able to go to a shop and mingle.

“Kate looked relieved, like it was a success going to a shop. It felt natural.”

The royal couple also spent Sunday morning watching Prince George, Princess Charlotte and Prince Louis taking part in a sporting event, according to The Sun.

Kate’s absence from public life, following abdominal surgery on January 16, has led to wild conspiracy theories on social media about her whereabouts and health.

Details of her condition have not been disclosed but Kensington Palace previously said it was not cancer-related and that Kate wished her personal medical information to remain private.

The online speculation increased after irregularities were spotted in a Mother’s Day photograph of Kate and her children, which led to the princess admitting to “editing” the image and apologising for any “confusion” caused.

The future Queen has been photographed in public twice since her operation.

In a picture published on March 4, she was a front-seat passenger in a car driven by her mother, Carole Middleton, in the Windsor area.

She was also spotted sitting next to William in a chauffeur-driven car last Monday, when he attended the Commonwealth Day service in London and she was driven to a private appointment.

It was reported at the weekend that she may speak about her health during public engagements which are not expected to resume until after Easter.

The Sunday Times reported a source as saying: “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.”

William and Kate’s children attend Lambrook School in Berkshire, which will start its summer term on April 17. Kate is expected to resume official engagements after this date.