Kate, 42, dressed down in a hoodie and leggings, carried her own shopping as she strolled through the car park at the shop.

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The footage emerged just hours after The Sun exclusively revealed Kate had spent Saturday shopping in Windsor.

She visited the Royal Farms Windsor Shop, a short walk away from her home near Windsor Castle.

The shop was launched in November 2001 after Prince Philip came up with the idea of selling goods from the Royal Estates.

Philip hoped that the shop would support local suppliers and promote top-notch British produce.

The Farm Shop has a butchery selling beef, pork, chicken and lamb from animals reared on the estate.

The Windsor estate boasts 200 pedigree Jersey milking cows, a Sussex beef herd, 140 breeding sows and 1,500 Lohmann Brown hens.

Its pure-bred Sussex beef is matured for 21 days to maximise tenderness and maturity.

Staff make their own sausages from the 600 pigs who pass through the butchery each year.

The Royal Farm pigs are reared outside during the summer months to boost their health.

A coffee shop offers a vast selection of cakes, cream teas, fresh cream patisseries, sandwiches, paninis and salads.

Using produce from the Farm Shop, it also sells salads, pies, pasties and quiche.

The Farm Shop also sells a number of delicious luxury hampers in padded wicker baskets.

Kate’s visit comes amid weeks of vile and bullying online behaviour where wild conspiracy theories have been spread unchecked.

Some even refused to believe our front page yesterday, despite Wills and Kate having being spotted by members of the public.

The Sun last week called on the world to ‘Lay Off Kate’ after she was harshly criticised for editing her Mother’s Day family photo.

‘MADNESS OF SOCIAL MEDIA’

We have chosen to both report her appearance in yesterday’s paper, and show the footage today, in a bid to bring an end to what the Palace has called the “madness of social media”.

Despite appearing fit and healthy, the princess remains under medical guidance to keep off work until next month.

No date has yet been given for a return to public duty after her abdominal surgery more than eight weeks ago.

It is understood she will return to work when she is good and ready.

The Sun revealed yesterday that the Princess of Wales was well enough to go shopping at Windsor Farm shop.

Nelson Silva, 40, who took the video, was shopping for steak at the farm shop when he spotted Kate and William in the bread aisle.

He told The Sun: “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 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.

“I just wanted to share with my family footage and show just how normal they were.”

He said the couple had obvious “chemistry” and “were super relaxed”.

“I didn’t feel like they were hiding who they were. But they didn’t quite know how people would react because there has been this build-up about their whereabouts and I got the sense they just wanted to be swift in there.

“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.”

Another eyewitness who watched the footage said it was “exactly what I saw”.

They added: “It’s just a woman shopping with her husband on a Saturday afternoon just like thousands of other couples across the country.

“I’m delighted that she is well and everyone else can see her back on her feet enjoying life again.”

On a busy weekend the princess also joined William to watch their children George, 10, Charlotte, 8, and Louis, 5, play sports together.

The first footage of Kate since Christmas Day shows the royal mum-of-three carrying a full shopping bag of goodies at the farm shop, just a mile from the Wales’ home at Adelaide Cottage, Windsor, on Saturday.

DRESSED-DOWN

She was filmed on a mobile phone for several seconds walking side-by-side with her husband from the shop back towards the car park.

Kate, usually dressed in latest fashions for official royal occasions, still looked elegant in her weekend wear as she donned a black three-quarter zip hoodie and matching black leggings.

Providing a glimpse of Kate’s regular weekend ‘dress-down’ look she also wore grey socks pulled up over the bottom of her trousers and black trainers.

Kate appeared to be in good spirits smiling and speaking to William as her hair blew in the wind.

Wills wore a beige baseball cap, paired with a black rain jacket, blue denim jeans and grey trainers.

The future King also carried his bag with goods in from the Windsor Farm Shop.

And The Sun’s royal photographer Arthur Edwards has told how the footage has “warmed my heart”.

He added: “It’s lovely to see Catherine looking so happy. People keep asking me, ‘Where’s Kate? How’s Kate?’

“These pictures are the answer. She’s obviously recovering well from the quite serious operation she had in January.

“The images of her smiling really warm my heart and I’m sure millions of others will be so pleased to see the Princess out and about.

“There have been so many rumours circulated about her on social media – but they can now be put to rest.”

Kensington Palace maintains Kate is “doing well” and will offer only significant updates as she recovers.

She spent 13 nights in hospital after requiring major surgery to her abdomen on January 17 at The London Clinic.

The palace said at the time: “The Princess of Wales appreciates the interest this statement will generate. She hopes that the public will understand her desire to maintain as much normality for her children as possible; and her wish that her personal medical information remains private.”

But in the past two months the internet has become a cesspit of unfounded gossip.

Conspiracy theories, which are far too ludicrous to be repeated in The Sun, spread around the internet.

Earlier this month a palace spokesman blasted the “madness of social media”.

Kensington Palace has always said she would be out of action until April. and only provide “significant” updates.

It is now believed that Kate may return after her children’s Easter school holidays in the middle of April.

SERIOUS SURGERY

It has been a difficult nine weeks since the princess was admitted to hospital.

William, 41, visited his wife every day in hospital every day and took time off work to help her settle back home at Adelaide Cottage.

He has been carrying on the school run in an effort to make life as normal as possible for his young family.

Kate spent half term school holidays in February at Anmer Hall, in Norfolk, with William and their children.

But speculation was rife after William pulled out of a thanksgiving service for his godfather at the start of the month citing a “personal matter”.

A photograph taken by a paparazzi photographer showing Kate in the passenger seat of a car with her mum Carole at the wheel was printed on a US showbiz website.

Kate apologised 24 hours after releasing a family photograph with her three children to mark Mother’s Day after it emerged she had edited.

The Photoshop mistake led to a torrent of abuse hurled online at the Princess of Wales.

The Sun understood the princess had been under pressure to produce the best picture she could, and led with the front page headline ‘Lay Off Kate’.

Sources close to the couple have indicated that they have been affected by the vile social media lies.

Kensington Palace last night declined to comment.

Experts have said the sightings are a “great sign” and show the country how well she is doing in her three-month recovery process.

An onlooker spotted the “happy” Kate and Wills before capturing video.

They said: “When I went inside I looked around and noticed them. They all looked happy.”

The Sun exclusively revealed her farm shop outing over the weekend – but no images were published of the trip at the time.

It comes after wild speculation and gossip about her health and whereabouts left Kate and Wills “devastated”.

Royal expert Hugo Vickers spoke exclusively to The Sun and revealed Kate’s short outings are a “good thing” and show the country she is doing well – adding cruel trolls are a “waste of time”.

He said: “We love her dearly. She does a fantastic job, and it’s a pity that people have taken this sort of attitude towards her.

“But supposing there could be, let’s say, some moving footage of her walking around the garden with the children, I would have thought something like that.

“I mean a shopping expedition, a visit to a school match. These are all very positive things.

“These are things which so-called normal parents do very regularly and totally. It’s a thoroughly good thing.

“We don’t need to know everything about Catherine. What we do long to know is that she’s well and up and about and soon you know, taking her place again, because she is an enormous asset to the Royal Family, much loved and much respected.”

It comes after Kate was embroiled in hurtful criticism over a Mother’s Day picture which she altered using Photoshop.

The royal was trolled online for her attempt to edit the snap with her kids.

Hugo said the public should “leave her alone” during what is understandably a fragile time.

He added: “The photograph was well received when it first came out, and then it was criticised later.

“But as the week went on, I think the general attitude suddenly over here in Britain and amongst intelligent people was, oh, come on, you know.

“Leave her alone, let her get better at her own pace.

“We admire her and respect her. And why are we treating her as if she’s some sort of a criminal for having, maybe, you know, tried to improve a photograph one way or another.

“It was very unattractive what was done last week, but I think the sympathy is absolutely there.”

Palace sources told The Sunday Times that Kate is keen to speak about her health battle — but only when she returns to frontline duties.

One friend said: “She and William are at their most open when out interacting with the public.

“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.

“They appreciate the public’s love and affection for their children and know there is a public appetite to see them on their birthdays.”

‘KATESPIRACIES’ 

The friend said Wills and Kate had been “shaken” by the online hysteria over her health and the fallout over her Mother’s Day snap.

But they said the couple refused to be pushed into revealing details.

The pal added: “They will want to be clear and more open, but they’ll do it when they feel ready.

“I would expect that to be her instinct and it will be her call. They are not going to be rushed.”

Kate was discharged 13 days after her January operation.

But as she recuperated speculation grew online over her health.

It was stoked further when William pulled out of a memorial service last month.

“Katespiracies” have ranged from her getting cosmetic surgery to appearing as a contestant on The Masked Singer.

Kate is unlikely to return until after April 17 when her children go back to Lambrook School, near Ascot, following the Easter holidays.

But last night, it was reported that she has not ruled out making a return to the public eye on Easter Sunday when she could join her family for the traditional walk to church in Windsor.