Little Ramona, who plays inquisitive Karen in the show, became the first child to win an award at the ceremony when she was named best female newcomer.
The programme also won the prizes for best sitcom and best British comedy.
Her ten-year-old co-star Daniel Roche, who was nominated for an award along with the show's other young star, Tyger Drew Honey, 13, said all three of them revelled in their moment in the limelight.
“People were asking for our autographs so Ramona and I were signing them like proper pop stars,” he said.
“Dawn French and David Tennant came to speak to us to tell us how much they liked our show and how good we were, which was a fantastic surprise.”
Hosted by Jonathan Ross, the night also saw appearances by British model Katie Price and former Baywatch babe Pamela Anderson.
Dressed in a flowing electric pink-and-black silk gown, Katie presented the trophy for best TV comedy actor to Simon Bird of Channel 4 comedy The Inbetweeners.
Pammie, meanwhile, wearing a low-backed patterned orange number, handed over a gong alongside her fashion designer pal Vivienne Westwood.
Elsewhere, retiring radio legend Terry Wogan, who presents the final edition of his BBC Radio 2 show on Friday, was honoured with a lifetime achievement award.
Harry Potter author JK Rowling also presented her friend Peter Kay with the outstanding contribution to comedy award.