- Sean Coughlan in London and Daniela Relf in Sheffield
- royal correspondent
The Prince of Wales is visiting a housing initiative in Sheffield on Tuesday to promote anti-homelessness projects.
The actress, who has been away from public life since Christmas, appeared relaxed and smiling in video images from a farmer's market in Windsor.
The prince will be hoping that the focus will return to one of his personal causes.
Prince William must have felt a sense of relief as he returned to his demanding job as a public official. I didn't hear any discussion about photos of his wife or family. That wasn't on the agenda.
The Prince and Duchess have had a difficult start to the year, with Duchess Kate undergoing abdominal surgery and spending time recovering. She plans to return to official duties after Easter.
Her health has been the subject of rumors circulating on social media, often wild conspiracy theories and internet sleuths.
So far we've seen grainy photos of the princess in a car, as well as a controversial photo published on Mother's Day, but there are concerns that the photo has been digitally altered. It was subsequently withdrawn by the photo agency. This only added to the frenzied anxiety about her health.
On Monday night, The Sun and other newspapers published photos of the royal couple shopping near their home in Windsor over the weekend, taken from video clips provided by the public.
The video, while not confirmed by Kensington Palace, suggests something far more optimistic and routine than the outlandish and outlandish claims being made on social media.
Rumors continue to circulate and speculation abounds as to whether it's really them, but this is the clearest evidence yet that Kate is doing well during her recovery.
Royal commentator Caroline Aston said new photos and the possibility of new conspiracy theories on social media will not help the Duchess of Cambridge recover from serious surgery.
She told Radio 4's Today programme: “The recovery has been long and difficult and it's been an emotional battle. Frankly, I don't think recent events have helped the Princess recover all that much.”
Kensington Palace has not denied that the photo is of the couple.
According to The Sun, the video was shot by a member of the public who could hardly have expected the royal couple to wander into a local store without expecting to be spotted.
But one reason Kensington Palace has been reluctant to confirm what would otherwise be a positive story is that it raises thorny questions about privacy.
This could set a difficult precedent for a couple hoping to maintain as much normal family life as possible, especially after the prince and princess's team have repeatedly asked for Duchess Kate's privacy to be respected while she recovers. be.
And last month, American publications published paparazzi photos of the princess, but British news outlets did not.
The difference in posting this photo may be the sheer amount of interest on social media, including false claims and wild speculation about the impending announcement.
It was so intense that conspiracy theories about conspiracy theories were flying around. Was this all orchestrated?
Prince William, Duchess Kate and their public relations team are feeling the pressure keenly as they hunker down in this bizarre media storm. They are millennial royalty and are not disconnected from what is being said.
The photo and the speculation surrounding it could also cast a shadow on William's trip to Sheffield.
The prince wants to focus on one of his most important projects, an ambitious five-year plan to tackle homelessness launched last year across six locations across the UK.
This included Sheffield, where the prince met people facing housing insecurity and heard about several projects to tackle a problem he believes is worsening.
He heard from families who have experienced homelessness and housing insecurity first-hand, and from housing associations and grassroots projects.
The Homewards initiative is Prince William's “flagship project” and he has a strong personal interest in how local partnerships develop, royal sources say.
To coincide with the visit, DIY chain Homebase is donating 1,500 'starter packs' containing furniture, paint and other items to support families moving into new accommodation.
The pack will be organized by housing campaigner Kwadjo Tuneboa, who said: “Safe, permanent, secure housing is paramount to ensure homelessness no longer becomes part of families' stories.” said.
Making families feel comfortable and “supporting their well-being” has also been proven to reduce future homelessness.
The Prince's visit has also been supported by some of Sheffield's landlords, who have earmarked 33 three- and four-bedroom properties for “families at risk of or experiencing homelessness”. is provided.
The Homewards project's approach is to bring together grassroots organizations, charities and commercial partners to form regional coalitions.
The scale of Sheffield's problem was highlighted by annual statistics showing 4,000 people or families apply to be registered as homeless. This is the city council's highest number ever and an increase of 500 people from the previous year.
Last month, the government announced £3m of funding to Sheffield City Council to tackle rough sleeping and homelessness.