Kate Middleton and Prince William Show Off Baking Skills on Surprise Visit With Medics and Patients

Kate Middleton and Prince William are in the party mood!

The royal couple recently surprised guests at a celebration marking the 75th anniversary of the U.K’s publicly-funded National Health Service and put the finishing touches to a birthday cake with the help of former Great British Baking Show finalist Alice Fevronia.

“The prince’s piping skills were less good than the princess’s, shall we say,” Fevronia tells PEOPLE about Kate and William’s baking skills after they both helped her decorate some cupcakes — with Kate also adding a topper to the bigger cake.

“They were just really fun,” Fevronia adds. “They were just having a fun time.”

“There was a real sort of sense of excitement and I think shock when the Prince and Princess walked into the marquee,” she adds about their surprise appearance at the NHS Big Tea party, which was hosted by NHS Charities Together, of which the royal couple — both 41 — are patrons.

“I was walking in behind them and ended up standing next to this lady and she almost grabbed me and just looked at me, went, ‘oh my gosh!’ because she was so shocked.”

During the event, the Prince and Princess of Wales met a number of patients and health workers as they helped prepare the party at the well-being garden of London’s St. Thomas’s Hospital in central London.

There was also time for them to have a light-hearted debate about whether cream or jelly should go on a scone first. For the record: Kate went for cream first, while for William it was simple — whatever is closest to him at the time, he said.

Along with marking the birthday of the NHS, Kate and William also attended the event to shine a light on NHS Charities Together for what it does to help those in the health service who need mental health and well-being support.

While the NHS provides free care at the point of need, there has always been some reliance on locally based charities to help fill gaps in the system and give further support to hospitals and medical centers.

Fevronia herself has many family members who have worked in the NHS and her partner is a pediatric doctor, working long stressful hours. “[The royal couple] were asking. How does he decompress and how does he relax? And I think it’s making sure that there’s people to talk to because it’s such a busy job,” she tells PEOPLE.

Party host and former Bake Off presenter Mel Giedroyc, adds that “The NHS is part of our DNA in this country. It is so precious. I hope, for the next 750 years, will grow and be nurtured and be loved and properly taken care of.”

As they mingled in the party, taking turns at various tables, one of those William sat with was the first baby born under the NHS — Aneira Thomas, from Swansea. She was even named after the man who forced through the setting up of the service in 1948, the then U.K. government minister Aneurin Bevan (she also shares his nickname ‘Nye’).

Thomas was born around a minute after midnight when her mother, Edna, appeared to follow one of the doctors’ pleas to “hold on” in order to become the first baby in the new health system. “It is central to who I am and I wanted to shout it from the rooftops,” she tells PEOPLE.

Thomas sat next to William for part of the tea. “I have always admired him – from when he was a teenager, growing up with their mother. And he is a fine figure of a man and as I held his hand I said ‘Do you realize how handsome you are?’ I think he said ‘I haven’t heard that before.’ I said ‘You could be the next James Bond!’ ” she smiles.

“What a wonderful backup for the NHS to have somebody like that coming in to share stories with us. It is a wonderful support,” she adds.

Thomas — whose son and daughter (who is a paramedic) were both saved by NHS staff after suffering separately from brain hemorrhages — adds of the service: “It is creaking at the seams but it is still a wonderful institution – truly amazing. It is free at the point of need and touches all of our lives,” she says.

Thomas handed William a copy of her book about her historic birth and the life that followed called Hold On Edna!

“Kate came over and said she’d read it – and she gave me a hug,” she tells PEOPLE. “It was like one of my grandchildren. It was the icing on the cake.”