The piece was painted by Dan Llywelyn Hall, whose portrait of the Queen last year was criticised as looking like a Spitting Image puppet.
A boy serving volleyballs at the Duke of Cambridge joked that he "felt sorry" for William after he was unable to return them.
Prince William performed an impromptu rendition of Living On A Prayer with Jon Bon Jovi and pop star Taylor Swift.
Despite lamenting his own "useless" video gaming skills, the Duke of Cambridge was brave enough to put them to the test in front of a room of onlookers today.
William, who was visiting BAFTA today to launch its Give Something Back appeal, also road-tested several games while attending BAFTA's Young Game Designers Workshop.
The Duke had his chance soon after his speech, trying games with titles such as Hamster: Accidental World Domination, Vacuum Panic and Smiley Dodgems, which were made by previous young design award winners.
William spent a good portion of his time trying his hand at Vacuum Panic, where the aim is to clean a bedroom before 'mum' comes in to check it.
"I'm not cleaning particularly well, I'm just going around in circles," he told designer Charlie Hutton-Pattermore as his fingers flicked over the iPad screen in front of him.
The Duke of Cambridge has hailed the "incredible" workof two surgical teams as he watched live operations at one the Royal Marsden in Chelsea.
Dressed in medical scrubs, he spent around 10 minutes viewing a breast reconstruction procedure for a female patient in her 80s.
As he was greeted by lead surgeon, Mr James, William said: "It's slightly surreal meeting you in this situation."
The Duke looked into a micro-vascular microscope placed above the body as he was talked through the surgical procedure, which usually takes six to eight hours to complete.
"That's amazing," he said as he peered through the microscope.
William is the first royal to view surgery at the Royal Marsden,which is a world-leading cancer centre specialising in all areas of diagnosis,treatment, care and research into the disease.
He has been president of the hospital trust since 2007, a position previously held by Diana from 1989 until her death in 1997.
The Duke and Duchess of Cambridge will welcome military supporters into their palace grounds today to mark London Poppy Day.
The royal couple will meet staff and volunteers taking part in the Royal British Legion appeal who will call at Kensington Palace as part of a tour across the capital on a 1960's Routemaster Bus.
The Duke of Cambridge will watch two live operations today at the Royal Marsden in Chelsea, west London, where he will view sections of a breast reconstruction procedure and the removal of a bladder tumour.
He is set to meet members of the surgical team involved in the operations in the Wolfson Surgical Suite, including the lead surgeons, Mr Stuart James and Mr Pardeep Kumar.
The Duke will be following in the footsteps of his mother, Diana, Princess of Wales, after she watched a heart operation at Harefield Hospital in Middlesex in 1996.
He will be the first royal to view surgery at the Royal Marsden, which is a world-leading cancer centre specialising in all areas of diagnosis, treatment, care and research into the disease.
The Duke of Cambridge will watch two live surgeries at The Royal Marsden NHS Foundation Trust in Chelsea today.
Prince William will visit The Wolfson Surgical Suite where he will view sections of a breast reconstruction and the removal of a bladder tumour.
He will then meet members of The Royal Marsden's surgical team involved in the operations, including the lead surgeons, Mr Stuart James and Mr Pardeep Kumar.
The Duke of Cambridge said London's staging of the Champions League final would inspire a generation through its "excellence" as he welcomed delegates to Uefa's 37th annual congress.
William declared himself "first and foremost" a football fan as he gave the opening speech at the annual conference of European football's governing body.
Tomorrow, Wembley Stadium will host the showpiece final of Europe's premier competition between Germany's two leading teams, Borussia Dortmund and Bayern Munich.
The Duke of Cambridge, who is president of English football's governing body the Football Association (FA), joked about who he thought would win the eagerly anticipated final.
He told delegates: "It is a great honour for us, the English FA, to host not just this prestigious congress, but of course - the real excitement - tomorrow's Champions League final.
My money is on Bayern Munich and two-nil. To host these events during our 150th anniversary year is truly special."
He went onto say: "Events like tomorrow's match are hugely important because they inspire through their excellence.
But what really counts is the work you all do at a grassroots level - investing in facilities; training coaches; and addressing discrimination to make the game open to everyone.
I know some of these issues are on your agenda today, and I welcome Uefa's determination to continue to improve European football for all."