The Princess of Wales has been filmed smiling and looking happy while out shopping with Prince William.

The couple were seen strolling through a car park on Saturday, in a video first published by The Sun, which said they were at Windsor Farm Shop, close to their home.

Kate, 42, was wearing a hoodie and leggings and carried her own shopping, while the Prince of Wales was dressed in a blue coat, jeans, trainers and a baseball cap.

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None of their three children – 10-year-old Prince George, Princess Charlotte, eight, and five-year-old Prince Louis – were with them.

The paper quoted shopper Nelson Silva, who shot the video, as saying they appeared “super relaxed”, while Kate also looked “happy”.

Mr Silva told the newspaper: “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 knew it from somewhere.

“Then William turned back and I thought ‘hold on I know this person’. I said to the staff, ‘I think it’s them’, as I paid.

“I went to the car and as they came out of the shop I just filmed them.”

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Another eyewitness who watched the footage said it was “just a woman shopping with her husband on a Saturday afternoon just like thousands of other couples across the country”.

The couple have, in recent weeks, faced social media speculation surrounding Kate’s health and whereabouts.

The princess spent time in hospital in January for abdominal surgery, shortly after her 42nd birthday.

Kensington Palace later confirmed the surgery was successful and she would be taking time to recover at home in Windsor.

Earlier this month, the princess apologised “for any confusion” after it emerged a Mother’s Day photograph of her with her children had been edited before being sent to picture agencies.

Kate said: “Like many amateur photographers, I do occasionally experiment with editing.

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

The image was circulated by a number of picture agencies on the day, before Reuters, Associated Press (AP), Getty Images and Agence France-Presse (AFP) told media outlets to “kill” the photo from their systems and archives.

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A week ago, the prince and princess were seen in public for the first time since the controversy, when they were pictured leaving Windsor. William went on to attend the Commonwealth Day service at Westminster Abbey, but Kate did not.

Meanwhile, the Duke and Duchess of Sussex’s individual profiles on the Royal Family website have been replaced with a combined one which is further down the page.

The joint profile includes some of the work they have done, such as Prince Harry’s Invictus Games and Sentebale charity in Lesotho, and Meghan’s work as a patron of several organisations.