- By Sean Coughlan & Daniela Relf
- State Correspondent
The Prince of Wales will visit housing initiatives in Sheffield on Tuesday to promote his homelessness programme.
After staying out of the public eye since Christmas, she was seen relaxed and smiling in video footage from a farm shop in Windsor.
Prince hopes to turn attention back to one of his personal causes.
It's been a rough start to the year for the prince and princess, with Catherine undergoing stomach surgery and spending time recovering. He is expected to return to public duties after Easter.
His health has been the subject of widespread and often wild conspiracy theories on social media and rumors by internet trolls.
So far we've seen a photo of the princess in a car and a hotly controversial image released for Mother's Day that was retracted by photo agencies after it was digitally altered. This only added to the feverish mood of uncertainty about his health.
On Monday night, the Sun and other newspapers published a photo of the royal couple shopping near their home in Windsor over the weekend, taken from a video clip provided by a member of the public.
The video, although not confirmed by Kensington Palace, suggests something more hopeful and everyday than the outlandish claims shown on social media.
It doesn't stop the rumor mill from circulating, and we can now speculate whether it's actually them, but it's clear evidence that Catherine has been doing well during her recovery.
Royal commentator Caroline Aston said new images and the possibility of new conspiracy theories on social media would not help Catherine's recovery from major surgery.
He told Radio 4's Today programme: “The recovery is going to be long and hard and it's a mental struggle too, and frankly I don't think recent events have helped the Princess's recovery that much.”
Kensington Palace did not deny the photo of the couple.
The Sun claims the video was taken by members of the public – and the royal couple could not have expected to wander into their local shop without expecting to be spotted.
But part of Kensington Palace's reluctance to ensure what would otherwise be a positive story is the thorny question it raises about privacy.
After the team around the prince and princess repeatedly asked for their privacy to be respected during Catherine's recovery, it could set a difficult precedent for the couple, who want to preserve as much normal family life as possible.
While American publications published paparazzi photos of the princess last month, UK newspapers did not.
The difference in running this film could be the sheer howl of interest on social media, with spurious claims of immediate announcements and wild speculation.
It was so serious, there were conspiracy theories about conspiracy theories. Is it all integrated?
Prince William and Catherine and their PR team are well aware of this pressure as they try to navigate this strange media storm. They are millennial royals and don't mince words.
This photograph and the accompanying speculation may overshadow William's trip to Sheffield.
The prince will want to focus on one of his most important projects – an ambitious five-year plan to tackle homelessness in six locations around England and launched last year.
That includes Sheffield, where the prince will meet people facing home insecurity and hear about some of the plans for what appears to be a worse problem.
A royal source says the Homewards initiative is Prince William's “flagship project” and he takes a personal interest in how its local partnerships develop.
To coincide with the arrival, DIY chain Homebase donated 1,500 “starter packs” of furniture, paint and other items to help families move into new accommodation.
Helping organize the packages was housing campaigner Kwajo Tweneboa, who said: “Safe, permanent and secure housing is vital to ensure that homelessness does not become part of a family's story.”
Making families feel comfortable and “supporting their well-being” has been shown to reduce future homelessness.
Some of Sheffield's landlords are also backing the prince's visit, with 33 three- and four-bedroom properties available for “families on the brink of or experiencing homelessness”.
The approach of the Homewards project is to bring together grassroots organisations, charities and business partners to form local alliances.
The scale of the problem in Sheffield was highlighted by annual figures showing 4,000 people or families applied to be registered as homeless, the highest figure for the council and up 500 on the previous year.
Last month, the Government announced £3m funding for Sheffield City Council to tackle rough sleeping and homelessness.