In her latest film, Victoria and Abdul, Dame Judi portrays the former queen as she lusts after a young Indian servant, played by 30-year-old Ali Fazal. Describing her instant chemistry with her co-star, she told Radio Times there was "no acting at all required".
"He is very, very tall. He is extremely beautiful and he is an utterly delightful, charming man ... and a good actor," she said. Dame Judi also recalled a "unbelievably rapturous scene" with fellow actor Tom Bell in the 1965 film He Who Rides a Tiger, adding: "That was quite a day. That was terrific."
Dame Judi met Mills in 2010 when he asked her to open a red squirrel enclosure at the British Wildlife Centre near her Surrey home.
But she admits she was not on the lookout for another partner following the death of her husband of almost 30 years Michael Williams in 2001. Fellow actor Williams, with whom she had daughter Finty, 44, passed away after a battle with lung cancer.
"I think if you were looking for something it might have been different, but I had no intention [of getting involved with another man]," she said.
Of Williams, whom she met on the set of sitcom A Fine Romance, she said: "I miss him but I talk a lot about him. Little things can still catch you unawares ...You can be laughing and quite suddenly it's as if somebody comes along with a hammer and you get these taps."