However, the British monarch had an even stranger response upon receiving the contraption, which, according to The Sun, consisted of a stuffed glove on a wooden lever.
"There were still one or two noisy students about in those days – the end of the Sixties, you know," Princess Anne began.
"And three of them pushed out of the crowd with this hand and it was a sort of stuffed glove, for want of a better expression, with a joint.
"And these three presented it to the Queen, I think thinking that they were being really rather daring and rather cheeky.
"And the Queen took it from them and said ‘Thank you very much, that is what I’ve always wanted!’
"And their faces literally dropped because it wasn’t quite the reaction they’d expected!"
The 93-year-old's role involves a lot of waving, which Princess Anne joked, "And of course, it is exactly what she’d always wanted," while imitating using the hand.
Author Robert Hardman, who spoke to the princess for his book Queen of the World, said: "The Queen was rather taken with it and I think it ended up at Balmoral. I don’t think she ever used it in public, but I hear it became a much-loved family joke."
Unfortunately, Anne revealed that the gift "got lost somehow."
"Someone’s sense of humour perhaps didn’t stretch as far as ours," the Princess Royal explained, before suggesting they send another one to the royal family.
In the interview, Princess Anne - who is the only daughter of Prince Philip and the Queen - also suggested there are different expectations of women in the Royal Family.
"It’s difficult, I always think, to take an intelligent interest and wear a grin," Princess Royal said.
When asked about her brother, Prince Charles, she said:
"But men can be more serious – they’re allowed to be.
"Women aren’t supposed to be funny either."