Janet Brown, who has died aged 87, wrote an autobiography in 1986 titled Prime Mimicker, and it is for her takeoffs of Margaret Thatcher that the impressionist will be best remembered. She was quick to add the Iron Lady to her repertoire when Thatcher became Conservative party leader in 1975, during Brown's run in the quickfire-impressions television show Who Do You Do? (1972-75) and its sequel, Now Who Do You Do? (1976).

As a result, she was hired to impersonate Thatcher alongside the small screen's top male impressionist of the time, Mike Yarwood, in Mike Yarwood in Persons (1977-81) and Look – Mike Yarwood (1971-76).

With Thatcher's ascent to the office of prime minister in 1979, Brown's own fame spiralled. As well as appearances on many entertainment shows, she was given her own programme, Janet and Company (1980-82). There seemed some irony in the fact that the final two episodes were postponed because of the Falklands war, which helped the real-life Thatcher to turn around her poor popularity ratings.

Brown was also a regular on BBC radio's The News Huddlines and played the role of prime minister, a clearly undisguised Thatcher, in the 1981 James Bond film For Your Eyes Only.

She even met and corresponded with Thatcher. "I was at Wembley in 1986 for a Conservative party conference," Brown recalled. "Afterwards, she came up to me and said, 'I know you could have delivered my speech better than I did, but was it all right?' She was always very sweet to me and she needn't have been. But, then, I used to be quite selective about the scripts I'd do. I was prepared to send her up, but not maliciously."

Born in the South Lanarkshire town of Rutherglen, outside Glasgow, Brown started doing impersonations as a teenager. She attended Rutherglen academy and, after second world war service with the ATS, went into variety.

In 1946, while taking part in rehearsals for a Jack Hylton revue, she met the actor Peter Butterworth, who was later to appear in the Carry On films. They married the same year, and she credited him with sharpening her sense of humour.

She was later cast in the writer James Bridie's West End stage play Mr Gillie (Garrick theatre, 1950) as the doctor's daughter Nelly Watson, who falls for the Scottish schoolmaster of the title, played by Alastair Sim – a production screened by BBC television. In the same year, she was seen doing impressions of the show-business figures Marie Lloyd, Kathleen Harrison, Jessie Matthews and Gracie Fields in the television variety show A Ray of Sunshine, presented by the comedian Ted Ray.

Brown made her film debut in the Glasgow shipyard drama Floodtide (1949) and followed it by appearing alongside Sim again in the comedy Folly to be Wise (1952), produced by Frank Launder and Sidney Gilliat. She also performed in episodes of the television sketch shows The Eric Barker Half-Hour and How Do You View?, starring Terry-Thomas (both 1952).

After further stage work and the role of the production secretary Janet in the radio show The TV Lark (1963) – a sequel to The Navy Lark, with the ship's crew running a television station – she had a straight role in Z Cars (1965) before regular appearances in The Dick Emery Show (1967-68) and the role of Joyce in the sitcom Mr Digby Darling (1969), with Sheila Hancock and Peter Jones.

Then, Brown's impressions found a showcase on television. As well as Thatcher, she was particularly remembered for impersonating Joan Rivers, Pam Ayres, Nana Mouskouri, Barbara Woodhouse and, in character, Dallas's Sue Ellen Ewing. This even brought Brown fame abroad, including Australia, where she performed cabaret and spoke at the Sydney Opera House – as Thatcher – during the country's bicentennial celebrations in 1988.

Her popularity inevitably waned with the demise of both television variety shows and Thatcher. Most of her later television appearances were in dramatic roles, in series such as Doctors (2003), Midsomer Murders (2004), Casualty (2005) and Hotel Babylon (2009).

Brown's final stage role was as Old Lady Squeamish in a West End production of The Country Wife (Theatre Royal, Haymarket, 2007).

Her husband died in 1979. Brown and Butterworth had two children, Emma, who died in 1996, and the actor Tyler, who survives her.

• Janet McLuckie Brown, actor and impressionist, born 14 December 1923; died 27 May 2011