Born in Ilford, East London, England and growing up in East Grinstead, Leeves trained as a ballet dancer and worked as a model, until she made her first film appearance as a topless angel in Monty Python's The Meaning of Life.

She was a regular on The Benny Hill Show (as one of "Hill's Angels") and appeared as a tourist with a baby in the David Lee Roth music video for the song "California Girls", but struggled for several years to establish herself. She became somewhat visible as the flighty record company employee on the syndicated sitcom Throb!.

She had a recurring role in the television series Murphy Brown which provided her first period of success, playing "Audrey", the loud and awkward girlfriend of producer Miles Silverberg (played by Grant Shaud). Leeves also appeared as the troublesome Marla the Virgin in four risqué episodes of Seinfeld: "The Virgin", "The Contest", "The Pilot" and "The Finale - Part 2". Moreover during this period Leeves was cast as Holly for the U.S. version of the science-fiction comedy Red Dwarf.

In 1993, she joined the cast of the television series Frasier where she had second billing. Leeves played the eccentric, forthright and allegedly psychic Mancunian Daphne Moon, and she became popular in this role. By the start of 2000-2001 season, Leeves was pregnant, and the writers incorporated her pregnancy into shows as weight gain due to her character's stress from her relationship with Niles. By the conclusion of Frasier, Leeves had received an Emmy Award nomination for her role and had become the highest-paid British actress in Hollywood.

Appearing less frequently in cinema, Leeves lent her voice to the animated film James and the Giant Peach (1996) and acted in the film Music of the Heart (1999).

In 2004 she hosted an episode of Have I Got News for You. When news was revealed that the BBC had flown 188 journalists over to cover the presidential election in the USA, she quipped, "I can't believe that the BBC would spend money flying people all the way across the Atlantic just for a television programme."

Besides her major work in television, Leeves is also remembered for her role in the 1985 movie To Live and Die in L.A., in which she portrayed a scorned bisexual involved in a steamy ménage à trois during which she was required to act as though she were having multiple orgasms in a comical way. Her character eventually runs off with the woman.