Sim was born in Edinburgh, the youngest child and second son of Isabella (née McIntyre) and Alexander Sim. His mother moved to Edinburgh as a teenager from Eigg, one of the Small Isles in the Hebrides, and was a native Gaelic speaker. His father was a Justice of the Peace and a successful tailor with a business on Lothian Road. Sim was educated at Bruntsfield Primary school, James Gillespie’s High School and George Heriot’s School. He worked – probably part-time – in his father’s shop and then for the men’s outfitters Gieve’s, displaying no talent for the retail trade. In 1918 he was admitted to the University of Edinburgh to study analytical chemistry, but was called up for army training.

After the end of the First World War in November 1918, Sim was released from military service. On his return home he told his family that he did not intend to resume his studies at the university, but instead would become an actor. His announcement was so badly received that he left the parental home, and spent about a year in the Scottish Highlands with a group of itinerant jobbing workers. Returning to Edinburgh, he took a post in the burgh assessor’s office. In his spare time, he joined poetry reading classes, winning the gold medal for verse speaking at the Edinburgh Music Festival. This led to his engagement to teach elocution at a further education college in Dalry, Edinburgh. He held this post from 1922 to 1924. After taking an advanced training course in his subject, in 1925 he successfully applied to the University of Edinburgh for the post of Fulton Lecturer in Elocution, which he held for five years.

While maintaining his university position, Sim also taught private pupils and later founded and ran his own drama school for children in Edinburgh. This developed his skills as a director and occasional actor. One of his pupils, Naomi Merlith Plaskitt, aged 12 when they met, became his wife six years later. The dramatist John Drinkwater saw one of Sim’s productions for the school and encouraged him to become a professional actor. Through Drinkwater’s influence, Sim was cast in his first professional production, Othello at the Savoy Theatre, London, in 1930; he understudied the three principal male roles (played by Paul Robeson, Maurice Browne and Ralph Richardson) and played the small role of the messenger.

Sim followed Othello with productions ranging from a musical revue to a medieval costume drama by Clifford Bax, in whose The Venetian he made his Broadway debut in October 1931. In 1932–33 he was engaged for sixteen months as a member of the Old Vic company, headed by Peggy Ashcroft. He performed in ten plays by Shakespeare, two each by Shaw and Drinkwater, and one by Sheridan. He began to attract the attention of reviewers. The Times said that in As You Like It Sim as Duke Senior and George Devine as Duke Frederick “endowed the dukes with the properly fabulous touch of fairyland”. In The Observer, Ivor Brown wrote that Sim’s Claudius in Hamlet had “a sly roguishness that was immensely alive.” During the Old Vic season, Sim married his former pupil, Naomi Plaskitt, on 2 August 1932. They had one daughter, Merlith Naomi.

For several months in 1934, Sim was incapacitated by a slipped disc, which was successfully treated by osteopathy. When he recovered, he made a strong impression on West End audiences as Ponsonby, a sycophantic bank director in the comedy Youth at the Helm. Ivor Brown called his performance “a joy … a marvellous mixture of soap and vinegar”. On the strength of this success Sim was cast in his first film, The Riverside Murder (1935), in the role of the earnest but dim Sergeant McKay. There followed a sequence of films, a mixture of comedies and detective stories, including Wedding Group (1936), in which Sim and his wife both appeared, he as a Scottish minister, she as the maid; Edgar Wallace’s The Squeaker (1937), after a stage production of the same piece; Alf’s Button Afloat (1938) with the Crazy Gang; also in 1938 he played a revengeful ex-con Soapy Marks in the Associated British Picture film The Terror, and the “Inspector Hornleigh” series (1939–41), as the bumbling assistant of Gordon Harker.

Sim and his wife Naomi promoted and encouraged young acting talent. Among their protégés was George Cole, who lived with them on and off from 1940, when he was 15 years old, until 1952, when he married and bought a house nearby. Cole appeared with Sim in eight films from Cottage to Let (1941), to Blue Murder at St Trinian’s (1957). An obituary of Naomi Sim noted in 1999: “Cole wasn’t the only youngster to benefit from the Sims’ generosity and love of youthful spirits. At least half a dozen others – ‘our boys’ as Naomi called them – mostly unhappy at home, have cherished memories of life at Forrigan, the welcoming woodland retreat built by the couple near Henley-on-Thames in 1947. They also found time to have a child of their own, Merlith, who lives [in 1999] at Forrigan with her family and next door to George Cole, who remained close to Naomi Sim to the end.”

In 1948, Sim was elected Rector of the University of Edinburgh. He held the post until 1951; when he stood down he was made an honorary Doctor of Law. He was appointed CBE in 1953, and refused a knighthood in the early 1970s. An English Heritage blue plaque was unveiled in July 2008 at his former home at 8 Frognal Gardens, Hampstead, by his daughter Merlith McKendrick at a ceremony attended by George Cole. There is a plaque commemorating Sim’s birth outside the Filmhouse Cinema in Lothian Road, Edinburgh.

Sim returned to substantial stage roles at the last Malvern Festival; in James Bridie’s comedy What Say They? he played Professor Hayman, making him, as The Manchester Guardian put it, “baleful as a shaven John Knox and lean as a buzzard … a grand performance”. This was the start of an association between Sim and Bridie that lasted until the latter’s death in 1951, with Sim starring in, and directing, Mr Bolfry (1943), The Forrigan Reel (1945), Dr Angelus (1947) and Mr Gillie (1950).

After Bridie’s death in 1951, Sim appeared in only two stage productions during the rest of the decade. The first was a revival of Bridie’s Mr Bolfry in 1956, in which Sim moved from the role of the puritanical clergyman to that of the Devil. The second was William Golding’s The Brass Butterfly, a 1958 comedy described by The Times as portraying the relations between an urbane Roman emperor (Sim) and a Greek inventor with wildly anachronistic scientific ideas (George Cole).

Sim’s performance in Scrooge (1951) is considered by many to be the best portrayal of the title character on screen, and it is among his best known film roles, particularly in the U.S. In the farcical The Belles of St Trinian’s (1954) he played the dual roles of Millicent and Clarence Fritton, the headmistress of St Trinian’s and her shady brother. Having originally accepted the part of Clarence, Sim agreed to play in drag as Miss Fritton when Margaret Rutherford proved unavailable, and the director and co-producer, Frank Launder could find no suitable actress as an alternative. His “Burke and Hare” film The Anatomist debuted on British TV (on “International Theatre”) on Feb. 6, 1956, and was later released theatrically in the U.S. in 1961, leading some reference sources to list it as a 1961 movie.

In 1959, Sim sued the food company H J Heinz over a television advertisement for its baked beans; the advertisement had a voiceover sounding remarkably like him, and he insisted that he would not “prostitute his art” by advertising anything. He lost the case and attracted some ridicule for his action, but he was conscious of the importance of his highly recognisable voice to his professional success. Brooke comments on Sim’s “crowning glory: that extraordinary voice. Only Gielgud rivalled his tonal control and sensitivity to the musicality of the English language.”

On television, Sim’s best remembered performance was probably as Mr Justice Swallow in the comedy series Misleading Cases (1967–71), written by A. P. Herbert, with Roy Dotrice as the litigious Mr Haddock over whose court cases Swallow presided with benign shrewdness. Sim returned to the cinema in 1971 as the voice of Scrooge in an animated adaptation of A Christmas Carol. The following year he appeared as the Bishop in Peter Medak’s The Ruling Class (1972) with Peter O’Toole, and in 1975 he played a cameo in Richard Lester’s Royal Flash (1975) with Malcolm McDowell. After playing Lord Harrogate in the 1976 Disney film Escape from the Dark, his last role was as the Earl in the 1976 remake of Rogue Male opposite Peter O’Toole, a role for which he literally climbed out of his sick bed, saying, “Peter needs me.”

On stage Sim returned to Pinero farce, playing Augustin Jedd in Dandy Dick at Chichester and then in the West End. Once again he co-starred with Patricia Routledge. His last stage appearance was in a return to the role of Lord Ogleby in a new production of The Clandestine Marriage at the Savoy in April 1975.

Sim died in 1976, aged 75, in London, from lung cancer. His widow Naomi lived until 3 August 1999. She published a memoir, Dance and Skylark: Fifty Years with Alastair Sim in 1987.