The Princess of Wales has admitted becoming a member of the royal family was something she never expected – but then she met and “fell in love” with William.

Kate made the admission when she joined a Dame Kelly Holmes Trust event in Bath and took on the double Olympic champion at a game of bean-bag noughts and crosses – but came out second best.

When the princess sat down for a chat with a group of schoolgirls from St Katherine’s School in Bristol supported by the charity, she opened up the floor to questions about herself.

Asked if she wanted to be a “royal” by a pupil, the princess replied it was something she had not expected but she “fell in love” with William.

Commenting afterwards about the pupils’ chat with the princess, Dame Kelly said she posed a question about Kate’s three children asking if she saw different “traits” in them, and the royal replied “Oh yes, definitely”.

The double Olympic champion said when the schoolgirls quizzed Kate about being a “royal”, the princess said it was something “she had to learn”.

Speaking for herself, Dame Kelly said: “A struggle to kind of know that you can be accepted and fit in, and still learning every day.”

The double Olympic champion said public speaking was not a “natural thing” to many people and, commenting on Kate, added “she said she’s still working that out”.

Dame Kelly founded her national youth development organisation on the belief that every young person needs a champion.

It pairs world-class athletes with youngsters who may have lack confidence or have other issues, so the sportsmen or women can pass on their winning mindset and help the children develop the skills and confidence they need to succeed in life.

The eight pupils from St Katherine’s School in Bristol were taking part in the On Track To Achieve programme, delivered by their athlete mentor, Paralympic gold medallist Liz Johnson.

When she first arrived, Kate, who is known for her competitive streak, took part in an outdoor game to relax everyone, joining some of the eight students aged 11-14 being supported by the trust, while the former sports star joined the remaining pupils on an opposing team.

In bright summer sunshine, each team member ran forward and threw a bean-bag onto a grid on the ground.

Kate’s team did their best but Dame Kelly’s players twice won and, after their first victory, the track and field star held her arms aloft and admitted she was “slightly competitive”, and the princess joked “You would never have guessed”.