The Princess of Wales has said her youngest son Louis is a keen rugby player as she joined England’s wheelchair rugby league team to celebrate their World Cup title.

Kate, patron of the Rugby Football League, hosted a reception for the team at Hampton Court Palace on Thursday afternoon to mark the victory in November’s tournament, which was England’s first since the inaugural competition in 2008.

Kate said she, William and their three children had watched the final on television, in which England narrowly defeated France 28-24.

She laughed as she told the England team: “You’ve set the bar high haven’t you? Which is good.”

Asked whether her children were interested in rugby, she said: “We’re always slightly competitive with each other. They all love sport and Louis is mad about rugby. They are at an age where they just love running around.”

The princess added: “I do it all: whenever I can squeeze in exercise I do, even jumping on the trampoline with the children before school.”

Kate then beamed as the players invited her and her family to join them in training.

“I’d love to come and play,” she said. “There’s no excuse now. We’re going to have to have a family training session.”

Kate, who took over the Duke of Sussex’s former role as England’s rugby league patron in February last year, spoke to players, their partners and the coaching staff in the palace’s garden room before posing with the World Cup trophy.

She then joined the full team for a squad photograph, saying: “I’m really proud and really grateful we got this opportunity, and best of luck for the training and the season and I promise I’m going to come and see you for some games.”

Head coach Tom Coyd said Kate told him that Louis in particular was a fan of the sport.

He told the PA news agency: “She said Louis is doing tag rugby at school. She was saying that it is quite basic at the minute, that he is just getting to grips with the passing and the running around.

“But when you are four-and-a-half you just want to get the ball and run in any direction.

“She actually said that he recognised quite a lot of the crossover with the rugby that he is doing because in tag rugby you have tags on your hips and in our sport we have tags on our shoulders.

“I just think she and her family connected really well.”

Coyd added: “She said it would be great for us to go and do an engagement session at the school where her children attend.”

England player James Simpson, who retired after the World Cup, told PA he was visited by the then-Prince of Wales in hospital in 2009 after losing both his legs above the knee in an IED explosion in Afghanistan, where he was serving as a lance corporal in the Yorkshire Regiment.

Simpson said: “That is what started my journey really of getting into wheelchair rugby league three-and-a-half years later and that was a huge turning point for me.

“It gave me that teamwork, that camaraderie that I lost when I got injured. Going out there in your England shirt and singing the national anthem is absolutely incredible for me as an ex-soldier.”