03/08/2013 12:52 BST | Updated 03/08/2013 14:42 BST

Prince William On The Royal Nappy Run (Pictures)

The Duke of Cambridge has lifted the lid on his first days of fatherhood as he made his first public appearance since the birth of Prince George at a charity polo match.

William took a break from parenting duties to play in the Audi Polo Challenge at Coworth Park, Ascot, Berkshire alongside brother Harry, admitting he would be picking nappies up on his way home.

Prince William accepts a gift for his new son

The 31-year-old, who scored the winning goal for his team, was presented with a mini polo stick for Prince George by Audi UK director Martin Sander after the match.

William jokingly asked if it was nappies, quipping: "I've got to pick some up on my way home."

The royal admitted it was "good to get out of the house" for an afternoon.

But meeting guests afterwards, he added: "I've got to make sure I'm not too late back."

Of his performance on the pitch, William admitted: "I was in baby mode out there, thinking about nappies, I wasn't really in the zone."

And asked about son George, who was born on July 22, he said: "He likes to move around a lot, he wriggles a lot, he keeps us on our toes."

The Audi Polo Challenge is held each year and this year was in aid of charities SkillForce and The Royal Marsden Cancer Charity, of which William is patron and president respectively.

Kate attended last year's match, along with the couple's puppy Lupo, to support William and Harry, but there was no sign of her today.

She is thought to be at her parents' home in Bucklebury, Berkshire, with Prince George.

Prince William quips about becoming a new dad

Yesterday Kensington Palace announced that the birth of the third-in-line to the throne had been formally registered after a registrar from Westminster City Council visited the palace.

William, 31, signed the birth register entry for his son, listing his and wife Kate's jobs as prince and princess of the United Kingdom.

The RAF search and rescue pilot is currently on paternity leave but is expected to return to work at some point next week.

His next official public engagement will be to visit the Anglesey Show later this month.

An announcement on his future plans is expected within the next fee months.

William and Harry, 28, who yesterday joked about how his nephew's birth had taken the pressure off him to settle down, both played on the four-man Audi Quattro team as they took on the opposition Audi Ultra team.

The royals were watched by guests including former England rugby player Matt Dawson.

Peter Cross, chief executive of SkillForce, an education charity which helps hard-to-reach children, who was in the crowd, said: "This is fantastic. It is the third time that Audi have had SkillForce as one of the sponsored charities for the royal polo and we are really grateful for that.

"It's fantastic that the Duke of Cambridge's first public outing since the birth of his child is playing polo and SkillForce is a beneficiary of that.

"It's interesting that his last public engagement before his wedding was with SkillForce as well.

"It is a very close relationship, he is a wonderful royal patrol and he takes a very close interest."

William took part in a polo match

Cally Palmer, chief executive of the Royal Marsden Hospital and Cancer Charity, said: "The wonderful thing is the duke is a really hands-on presence at the hospital, he comes and visits, he takes a particular interest in the children that we treat at the Royal Marsden.

"The duke and duchess have been enormously generous with their support for us."

"I am so happy that they have their son now and their support, from both of them, is amazing."

She said the huge attention drawn by the William and Kate and their son meant the hospital would also be able to draw more attention to its work to find better ways to treat and diagnose patients.

Today's event was the 11th annual Audi Polo Challenge - its first included both William and Harry as well as their father the Prince of Wales.