Filmed by a member of the public on Saturday, it was the first footage of the Princess of Wales taken since Christmas Day. Kensington Palace has not denied that the video is genuine, but has declined to comment on a matter it regards as being the royals’ private time.

“If that video of Catherine sort of walking quite briskly with a shopping bag doesn’t put an end to this frankly wild and baseless speculation, then I’m not sure what will,” said Katie Nicholl, royal author and correspondent at Vanity Fair magazine.

Since she was hospitalised in January, Catherine’s office has stuck to its official line that the princess was recovering well and that it would only provide significant updates, maintaining the royal mantra of “never complain, never explain”. The princess was not expected to return to official duties until after Easter which falls on March 31.

However, Catherine’s absence has led to online rumours, and her apology this month for editing a photo taken by William of her and her three children to mark Mother’s Day only sparked further intrigue.

“A lot of people out there didn’t seem to want to believe that the simple truth of the matter was that she was at home recuperating from a clearly serious abdominal surgery,” Nicholl said.

William visited Sheffield in northern England on Wednesday (AEDT) to unveil new investment in his scheme to tackle homelessness, one of his main campaigning themes.

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Looking relaxed, he laughed and joked with staff and volunteers, and later referred to Catherine during discussions about homelessness and early childhood, one of his wife’s key projects.