The Princess of Wales emphasised with fellow parents as she told of "nerve-wracking" trips to the hospital with her own children.
The Princess walked the same route as the children visiting the centre, including rooms offering pre-surgery checks, operation theatres and recovering areas.
Speaking with one family in a pre-op cubicle, Kate said: "It’s always nerve-wracking as a parent; I’ve taken mine into hospital for different things. You're always at least worried but you’ve got a great team (here)."
In the recovery area, the royal also met four-and-half-year-old Saya Stephenson, who was resting in bed after an operation that morning to remove excess skin for her ears.
The Princess hugged her mother, Miwa Stephenson, who said she had been anxious about the surgery despite it being a relatively minor procedure.
Kate said: "It's always a worry though for a parent. We have to keep our cool. It's so hard."
Housed in the new Children’s Day Treatment Centre, the space-themed facility has two operating theatres, and will help the hospital to treat an additional 2,300 children per year.
Ella Moth, nine, and Chloe Morley, ten, joined the Princess to cut the ribbon on the door of the Children's Day Surgery Unit, to mark its official opening.
Ella, who won a competition to design the artwork for the new unit, said her space-themed drawings were inspired by the death of her father, Piers, who she said has now "gone to the stars". Her father was treated for brain cancer at Guy’s hospital before he died in 2021.
Kate, who has been patron of Evelina London since 2018, asked the youngster: "How does it feel to have your design on the wall for other children to enjoy, being an inspiration for loads of other kids?"
Ella replied: "I didn't think it would ever happen!"
Gubby Ayida, Chief Executive of Evelina London, said: “We were thrilled to be joined by our Royal Patron, The Princess of Wales, to officially open our Children’s Day Surgery Unit.
"We put children, young people and families at the heart of everything we do, and you especially feel that when coming into our new unit.
"It was lovely to have this recognised with The Princess of Wales today [Tuesday 5 December], who values the importance of having a supported and nurturing environment for children through her work with The Royal Foundation Centre for Early Childhood."
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