Oscar-winning British actor Dame Maggie Smith, star of Downton ...

He also paid tribute to her “warmth and wit that shone through both on and off the stage”, posting a photograph of him sharing a joke with the actress.

Prime Minister Keir Starmer also called her a “true national treasure” while the Bafta TV and the film academy saluted “a legend of British stage and screen”.

Born in 1934 in Oxford in central England, the daughter of an Oxford professor of pathology, Smith made her stage debut in 1952 with the Oxford University Dramatic Society.

She won a best actress Oscar for the 1969 drama The Prime of Miss Jean Brodie based on Muriel Spark’s novel, and best supporting actress for her role in the 1978 Neil Simon comedy California Suite.

“An intensely private person, she was with friends and family at the end,” her sons, both actors, said.

“She leaves two sons and five loving grandchildren who are devastated by the loss of their extraordinary mother and grandmother,” they said, adding their thanks for all the “kind messages and support” they had received.

Famed for her scene-stealing charisma, Smith’s long and successful career got started with a string of successes in London’s West End and on Broadway in the 1950s.

She famously appeared opposite Laurence Olivier in an adaptation of Shakespeare’s Othello in 1959.

This led to her joining Olivier’s celebrated 1960s National Theatre company where she earned critical acclaim alongside her husband, the actor Robert Stephens.

Smith’s marriage to heavy-drinking Stephens, with whom she had her two sons, collapsed in 1973 and they divorced two years later.

She remarried shortly after to the screenwriter Beverley Cross, who died in 1998.

Despite her serious acting reputation, Smith also appeared in lighter Hollywood hits such as 1992′s Sister Act, and 1993 sequel Sister Act 2.

Whoopi Goldberg, the lead actress in both films, wrote on Instagram that “Maggie Smith was a great woman and a brilliant actress”.

“I still can’t believe I was lucky enough to work with the ‘one-of-a-kind’,” she added.

In recent decades, some of her best known films included Gosford Park (2001), The Best Exotic Marigold Hotel (2012) and The Lady in the Van (2015).

Her work on the wildly popular Downton Abbey and the Harry Potter films also introduced her to a younger generation.

Such was the appeal of Downton Abbey she said in 2017 she could no longer go out without being recognised.

“It’s ridiculous – I led a perfectly normal life until Downton Abbey,” she told the British Film Institute. “I would go to theatres, I would go to galleries and things like that on my own. And now I can’t,” she said.

Julian Fellowes, creator and writer of Downton Abbey, said Smith had a “marvellous instinctive grasp, she could make you cry your eyes out one minute and laugh like a drain the next without turning into someone different.

“I realised I was working with a great genius,” he added.

Actor Hugh Bonneville, who played the son of the dowager duchess in the period drama, said: “Anyone who ever shared a scene with Maggie will attest to her sharp eye, sharp wit and formidable talent.

“She was a true legend of her generation and thankfully will live on in so many magnificent screen performances. My condolences to her boys and wider family.”

Smith was made a Dame of the British Empire in 1990 by Queen Elizabeth II.