Among the iconic figures of the 1960s – the Beatles, Bobby Moore lifting the World Cup and Sean Connery as James Bond – was the actor Diana Rigg. Her role as the secret agent Emma Peel in The Avengers on ITV, magnetically sexy in trademark black leather jumpsuit, was truly a sign of the times.

Rigg, who has died aged 82, often said she was unhappy on the series, claiming that her only friends were Patrick Macnee, her co-star as the bowler-hatted gentleman spy John Steed, and a television company chauffeur. But the on-screen chemistry with Macnee was palpable, and Rigg drew a scintillating portrait of a woman who knew her own mind as well as her own strength.

She had succeeded Honor Blackman (as Cathy Gale) as Steed’s independent sidekick, and appeared in three series of The Avengers between 1965 and 1967, during which period she was also one of the founding members of the Royal Shakespeare Company, playing many lead roles at Stratford-upon-Avon and at the Aldwych theatre in London between 1961 and 1966.

If Emma Peel was a career-defining role in the public eye, Rigg was never seduced from her dedication to the stage, although she expressed disappointment at a film career that never took off. Tall, elegant, vocally mellifluous and often strikingly acerbic, she could play tart comedy roles as easily as melting heroines, and in the latter part of her career she revealed untold depths of savagery and resilience with a series of award-winning performances in works by such masters as Euripides, Edward Albee, Jean Racine and Tennessee Williams.

She renewed her television stardom when, between 2013 and 2017, to the rejoicing of a new legion of fans, she played the ruthless Lady Olenna Tyrell in Game of Thrones, a fearsome matriarch whose political machinations in the cause of keeping the House of Tyrell’s legacy intact were of a Shakespearean malice and complexity. After completing the recording she underwent heart surgery, and wryly remarked after her recovery that God must have said, “Send the old bag down again, I’m not having her yet.”

Rigg was born in Doncaster, South Yorkshire, but raised for the first eight years of her life in Jodhpur, India, where her father, Louis, was a railway engineer. She knew both the privileges of the British Raj and the hardship of living in reduced circumstances in postwar Leeds, where she returned with her older brother, Hugh, and her mother, Beryl (nee Helliwell), in 1945. Her parents had been in India since 1925, and her father rejoined the family in 1948.

By then she was boarding at Fulneck girls’ school in Pudsey, where her aptitude for acting propelled her to London and Rada. She first appeared at the Theatre Royal, York, in a Rada production of Bertolt Brecht’s Caucasian Chalk Circle, and, after further seasons in York and Chesterfield, went straight to Stratford in 1959, where Peter Hall was planning the launch of the RSC the following year.

Rigg made her London debut with the RSC in Jean Giraudoux’s Ondine (playing second fiddle to Leslie Caron, then Hall’s wife) in 1961, and over the next few years, as part of a brilliant nucleus of young actors that included Judi Dench, Ian Holm, Ian Richardson and Tony Church, she helped define the new RSC adventure in a series of dazzling performances.

These included a spirited, diaphanously clad Helena in A Midsummer Night’s Dream (later filmed by Hall), Bianca in The Taming of the Shrew, Adriana in The Comedy of Errors (a thrown-together comedy riot that returned year after year to the repertoire), a sweet but determined Cordelia to Paul Scofield’s titanic King Lear, directed by Peter Brook – the production toured many European cities – and a radiant, striding Viola in Twelfth Night, a shimmering androgyne and first cousin to Emma Peel.

Her West End “commercial” debut followed in a lumpen 1970 retelling of the Abelard and Heloise story in which she starred opposite Keith Michell in both London and New York.

The National Theatre came calling in 1972 for the Old Vic premiere of Tom Stoppard’s brilliant man-on-the-moon philosophical comedy Jumpers, in which Rigg was languorously draped across a crescent moon as Dottie Moore, the dissatisfied, romantic wife of Michael Hordern’s dotty George Moore. The play was a sensational success, followed in 1973 by an equally stunning Célimène, the bitchy hostess in Tony Harrison’s brilliant rhyming update of Molière’s The Misanthrope.

Her tragic muse remained dormant at this time, despite a brave stab at Lady Macbeth opposite a curiously listless Anthony Hopkins (Old Vic, 1973), and she struck more comic sparks off Alec McCowen in a John Dexter revival of George Bernard Shaw’s Pygmalion in the West End in 1974. Dexter had accused her of being “hard” and as easy to negotiate as the north face of the Eiger, but she always listened to his uncomfortably critical concerns.

After scoring another hit with Harrison in his Racine rewrite, Phaedra Britannica, in the last season of the National at the Old Vic in 1975, and giving birth to a daughter in 1977, she cut all ties with the two subsidised monoliths and appeared in the West End as Ruth Carson in Tom Stoppard’s Night and Day (1978) at the Phoenix (“I’m with you on the free press. It’s the newspapers I can’t stand,” was Ruth’s languidly pleasant view in the play’s discussion of journalistic ethics); in an all-star Heartbreak House with Rex Harrison at the Haymarket in 1983; and in an even more lavish Cameron Mackintosh production of James Goldman and Stephen Sondheim’s Follies at the Shaftesbury in 1987.

Although she was a “Bond girl” in one of the lesser James Bond movies, On Her Majesty’s Secret Service (1969), with George Lazenby, and Vincent Price’s avenging daughter, Edwina Lionheart, in the comedy horror movie Theatre of Blood (1973) – a role her daughter, Rachael Stirling, wittily reprised in the National Theatre stage version in 2005 – her career on celluloid stuttered. She appeared as a murdered actress in Guy Hamilton’s all-star Poirot mystery Evil Under the Sun (1982) and a mother superior in the remake of Somerset Maugham’s The Painted Veil (2006).

Otherwise, she made sporadic yet powerful incursions on television: as Regan to Laurence Olivier’s valedictory King Lear (1984), Lady Dedlock in Bleak House (1985), an obsessive mother in the BBC mini-series Mother Love (1989) for which she won the Bafta best actress award, and as Mrs Danvers in Rebecca (1997), co-starring with Emilia Fox and Charles Dance, for which she won an Emmy when it was broadcast in the US.

But it was in the theatre that Rigg crowned a remarkable career, with a string of scintillating performances at the Almeida, Islington, during the 90s: first, in John Dryden’s All for Love, then as a rampaging Medea (both 1991), with the latter transferring to the West End and Broadway, where she won a Tony award; as a ferocious Martha in Albee’s Who’s Afraid of Virginia Woolf?, with a ginger hairstyle and leopardskin print slacks, fighting to the near-death with David Suchet in 1996; and then as both Racine’s Phaedra and his bigamous Messalina in Britannicus in 1998.

These performances attracted critical acclaim and a clutch of awards from the Evening Standard, the Variety Club and the South Bank Show and, for good measure, she slotted in a slightly less successful Mother Courage at the National Theatre in 1995.

Rigg returned to the National in 2001 to play Simon Russell Beale’s exotic mother in Charlotte Jones’s Humble Boy, and continued in extravagant vein as Mrs Venable in Michael Grandage’s 2004 West End revival of Tennessee Williams’s Suddenly Last Summer, followed three years later by the less-than-urgent stage version of Pedro Almodóvar’s All About My Mother at the Old Vic in 2007.

She had lived for some years in a chateau in a village south of Bordeaux in France, and one of her neighbours there, the producer Duncan Weldon, was instrumental in arranging her casting at the Chichester Festival theatre in 2008 and 2009, in roles that should have been ideal: Ranevskaya in Chekhov’s The Cherry Orchard and Judith Bliss in Noël Coward’s Hay Fever, but neither production was a success and both failed to arrive in the West End.

But she was superb when she stepped into another Chichester revival, Shaw’s Pygmalion, at the Garrick in 2011, returning to the play she first graced in 1974, as Mrs Higgins, alongside Rupert Everett and Kara Tointon in Philip Prowse’s beautiful production. Her Mrs Higgins in a 2018 production of My Fair Lady at Lincoln Center in New York, the first Broadway revival of the musical in 20 years, earned her a Tony nomination.

In 2014, on the Edinburgh festival fringe, she gave an anecdotal solo show based on her 1982 book of rotten reviews, No Turn Unstoned.

Later screen appearances were in an episode of Doctor Who, The Crimson Horror, in 2013, with her daughter (whom, in character, she blinded); as onscreen mother to Rachael in the second and third series of the TV comedy Detectorists (2015 and 2017); the outspoken Duchess of Buccleuch in Daisy Goodwin’s second series of Victoria for ITV in 2017; and, briefly, as an imperious aristocrat in Andy Serkis’s movie Breathe (2017) starring Andrew Garfield and Claire Foy. She will appear as Mrs Pumphrey, owner of the ailing peke Tricki Woo, in the remake of All Creatures Great and Small currently showing on Channel 5.

Rigg was chancellor of Stirling University for 10 years from 1997, and Cameron Mackintosh visiting professor of contemporary theatre at Oxford University in 1999, and she published a second book, So to the Land, an anthology of countryside poetry, in 1994.

She was appointed CBE in 1988 and made a dame in 1994.

After a long relationship with the television director Philip Saville, in 1973 Rigg married the Israeli artist Menachem Gueffen. They divorced in 1976 and in 1982 she married the Scottish laird Archie Stirling, a former army officer who became a theatre producer. When it emerged that Stirling was having an affair, Rigg sued for divorce and took his suits to the nearest Oxfam shop.

She is survived by Rachael and a grandson, Jack.

• Enid Diana Elizabeth Rigg, actor, born 20 July 1938; died 10 September 2020