Margolyes was born in Oxford on 18 May 1941, the only child of Ruth (née Walters; 1905–1974), an English property investor and developer, and Joseph Margolyes (1899–1995), a Scottish physician from the Gorbals area of Glasgow. She grew up in a Jewish family, with ancestors who moved to the UK from Belarus and Poland. Her great-grandfather, Symeon Sandmann, was born in the Polish town of Margonin, which Margolyes visited in 2013. She attended Oxford High School and Newnham College, Cambridge, where she read English. There, in her 20s, she began acting and appeared in productions by the Cambridge Footlights. She represented Newnham College in the first series of University Challenge, where she may have been one of the first people to say “fuck” on British television; she claims to have used the word in frustration on the show in 1963.

In 1974, she appeared with Kenneth Williams and Ted Ray in the BBC Radio 2 comedy series The Betty Witherspoon Show.

Margolyes’ first major role in a film was as Elephant Ethel in Stand Up, Virgin Soldiers (1977). In the 1980s, she made appearances in Blackadder opposite Rowan Atkinson: these roles include the Spanish Infanta in The Black Adder, Lady Whiteadder in Blackadder II and Queen Victoria in Blackadder’s Christmas Carol. In 1986, she played a major supporting role in the BBC drama The Life and Loves of a She-Devil. She won the 1989 LA Critics Circle Award for Best Supporting Actress for her portrayal of Flora Finching in the film Little Dorrit (1988). On American television, she headlined the short-lived 1992 CBS sitcom Frannie’s Turn. In 1994, she won the BAFTA Award for Best Supporting Actress for her role as Mrs Mingott in Martin Scorsese’s The Age of Innocence (1993).

In 1989, Margolyes co-wrote and performed a one-woman show, Dickens’ Women, in which she played 23 characters from Dickens’ novels.

She played Professor Sprout in Harry Potter and the Chamber of Secrets released in 2002. In a 2011 interview on The Graham Norton Show, in regard to her fellow castmembers, Margolyes claimed that she liked Maggie Smith, but rather bluntly admitted that she, “didn’t like the one that died”, meaning Richard Harris.

In 2002, Margolyes was honoured by Queen Elizabeth II in the New Year honours list as an Officer of the Order of the British Empire (OBE) for Services to Drama.

In 2004, Margolyes played the role of Peg Sellers, the mother of Peter Sellers, in the Golden Globe winning film The Life and Death of Peter Sellers.

She was one of the original cast of the London production of the musical Wicked in 2006, playing Madame Morrible opposite Idina Menzel, a role she also played on Broadway in 2008.

Margolyes is a supporter of Sense (the National Deafblind and Rubella Association) and was the host at the first Sense Creative Writing Awards, held at the Charles Dickens Museum in London in December 2006, where she read a number of works written by talented deafblind people.

In 2009, she appeared in a new production of Endgame by Samuel Beckett at the Duchess Theatre in London’s West End.

In 2011, Margolyes recorded a narrative for the album The Devil’s Brides by klezmer musician-ethnographer Yale Strom.

Margolyes is openly gay. On becoming an Australian citizen on Australia Day 2013, she referred to herself as a “dyke” live on national television and in front of then-prime minister Julia Gillard. Since 1968, she has been in a relationship with Heather Sutherland, a retired Australian professor of Indonesian studies. They divide their time between homes in London and Kent in England, Robertson in Australia, and Tuscany in Italy.

In 2014, she voiced Nana in the Disney Junior animated series for pre-school-age viewers Nina Needs to Go!

Margolyes is a member of the Labour Party and is registered to vote in Vauxhall. In August 2015, she was a signatory to a letter criticising The Jewish Chronicle’s reporting of Labour leader Jeremy Corbyn’s alleged associations with antisemites. In November 2019, she endorsed the Labour Party in the UK general election because of their policies on the NHS. Later in the month, along with other public figures, she signed a letter supporting Corbyn and describing him as a “beacon of hope in the struggle against emergent far-right nationalism, xenophobia, and racism in much of the democratic world”.

In January 2016, she appeared in The Real Marigold Hotel, a travel documentary in which a group of eight celebrities travel to India to see whether retirement would be more rewarding there than in the UK. The series was reprised for two Christmas Specials The Real Marigold On Tour, from Florida and Kyoto. She narrated the 2016 ITV documentary about Lady Colin Campbell entitled Lady C and the Castle.

In December 2017, Margolyes appeared in the second season of The Real Marigold On Tour to Chengdu and Havana. She appeared in the first episode of the third season when she travelled to St Petersburg, Russia with Bobby George, Sheila Ferguson and Stanley Johnson.

In January 2018, Margolyes hosted a three-part series for the BBC titled Miriam’s Big American Adventure, highlighting the citizens of the US and the issues facing the nation.

Since 2018, Margolyes has portrayed Mother Mildred in the BBC One drama, Call The Midwife.

She played Miss Shepherd in a 2019 production of The Lady in the Van for the Melbourne Theatre Company in Melbourne in Australia.