Prince William and Kate Middleton in Rare PDA
05/11/2009 AT 11:20 AM EDT
"William spent about 40 minutes at the party after his match, and then picked up Kate and they wandered back to the car," says an onlooker. "He put his left arm around her back and there was plenty of smiling between them."
During the match, Kate sat with her sister Pippa and one of William's best friends, Tom van Staubenzee – whose family charity was one of the beneficiaries of the afternoon.
Middleton, 27, didn't show much reaction during the match – which William and Prince Harry's team, Umbogo, won by four goals to three. "She was just enjoying the sunshine and the game," says the bystander.
Sunday's event, sponsored by Audi, raised money for three of the princes' pet causes: Harry's Sentebale charity for the African nation of Lesotho; the Child Bereavement Charity, of which William, 26, is a patron; and the Henry van Straubenzee Memorial Fund, of which both princes are patrons.