The actor, 59, earned the accolade for her services to drama, as announced when she was recognised on the Queen’s Birthday Honours list in June.
Thompson collected the honour from the Duke of Cambridge and admitted she “sniggered” during the ceremony.
“I love Prince William, I’ve known him since he was little, and we just sniggered at each other,” she said.
“I said, ‘I can’t kiss you, can I?’ And he said, ‘No don’t’!
“If you’re first up you have to be more formal on such an occasion, but he’s looking wonderful and doing so well.
“He said, ‘This day isn’t about me, it’s about you’.
“It’s really lovely because I’ve always loved the boys and I’ve always been a long-term correspondent with their dad, it’s a very lovely feeling.”
Dame Thompson wore an emerald Stella McCartney suit, having purposefully picked a British designer, and sported a Fawcett Society equal pay badge.
“I’m very outspoken, politically, I’m a card-carrying feminist, human rights advocate, so good for them, because the establishment need more people who can speak up for those things,” the Oscar-winning actor said.
Thompson now hopes to use her damehood to raise awareness for holiday hunger, which sees children going hungry during school holidays.
“This is a very rich country with hundreds of thousands of children who don’t get enough to eat,” she said.
“I’m sorry, but that’s just rubbish.
“I’m going, why isn’t this top of the list? We have kids begging in schools for leftover food, that’s just awful.”
The dame won the Academy Award for Best Actress and the BAFTA Award for Best Actress in a Leading Role for her part in the 1992 romantic drama Howards End.
The 1995 adaptation of Sense And Sensibility, for which she wrote the screenplay in addition to starring as Elinor Dashwood, earned her the Academy Award for Best Adapted Screenplay and the BAFTA Award for Best Adapted Screenplay.
Additional reporting was provided by agencies.