Her earliest film role was as Mary McGregor in the 1969 British film The Prime of Miss Jean Brodie. In this role, like her fellow young actors, she had to portray the character at ages ranging from 11 to 18.

In 1970, she co-starred with Angela Lansbury and Michael York in Something for Everyone, and also starred in Danny Jones (1972) with Frank Finlay. Her other film roles have included the TV movie The Bunker (1981), Deal of a Lifetime (1999), Crazy as Hell (2002), Garfield: A Tail of Two Kitties (2006), Hannah Montana: The Movie (2009) and The Five-Year Engagement (2012). In 2014 she voiced Mrs. Goggins in Postman Pat: The Movie, and portrays Sister Serpent in the Halloween themed slasher film 31 (2015).

Carr received a Laurence Olivier Award nomination in 1977 for her performance as Mary Mooney in the comedy Once a Catholic. She joined the Royal Shakespeare Company in 1978, receiving a second Olivier nomination in 1982 for A Midsummer Night's Dream and appearing in The Tempest, As You Like It, Much Ado About Nothing, The Merchant of Venice and The Merry Wives of Windsor. She played Wendy in the 1982 RSC adaptation of J. M. Barrie's Peter Pan at the Barbican in 1982 and appeared opposite Maggie Smith in the 1985 production of Congreve's The Way of the World.

In 1980 she appeared as Rita in National Pelmet, series two opening episode of critically acclaimed drama Minder (UK, 1979–1994). She had a featured part as "Louise" in the US version of TV series Dear John (1988–92).

In 1985, she voiced the dual role of Computer and its Inner Voice in the Doctor Who radio series Slipback (UK, 1985). In 2008, she voiced the character of Grandma Winifred Fletcher in the American Disney animated television series Phineas and Ferb. She also voiced Lady Cecelia in Familias Regnant universe Heris Serrano trilogy graphic audio book.

In 1987 she moved to the United States while touring with the Royal Shakespeare Company's production of The Life and Adventures of Nicholas Nickleby. From 2006 to 2009 she played Mrs. Brill in Mary Poppins on Broadway. Jane was part of the original cast of A Gentleman's Guide to Love and Murder, the Tony Winner for Best Musical in 2014. She played the part of Miss Shingle. In August 2014, Jane left the role, which was given to Carole Shelley.

In 1994 she played the quotable Timov (vomit spelled backwards), daughter of Al-ghul (Arabic: الغول, the ghoul) in the episode "Soul Mates" on US TV series Babylon 5. She continues to play occasional roles on television, including Fran Metzgar in Curb Your Enthusiasm (US, 2000), besides her voice work. In 2006 she served as both body double and voice Actress of "Tabitha Lenox" on the US daytime drama Passions when Actress Juliet Mills was on a brief vacation.

She also provides the voice of Mama Cosma in the animated series The Fairly OddParents (US and Canada, 1998).

Carr appeared on an episode of US TV series Friends, "The One with Ross's Wedding", and on three episodes of Gilmore Girls (US, 2000–2007).

In 2002 she played the part of Malcolm Reed's mother, Mary Reed, in the episode "Silent Enemy" of the US TV series Star Trek: Enterprise.

In 2012, she again played a nanny, this time as Mrs. Buckminster in a Season 8 episode of How I Met Your Mother.