Sims was born in 1930, the daughter of John Henry Simms (1888-1964), station master of Laindon railway station in Laindon, Essex, and his wife Gladys Marie Sims, née Ladbrook (1896-1981). Sims’ early interest in being an actress came from living at the railway station. She would often put on performances for waiting passengers. She decided that she wanted to pursue show business during her teens, and soon became a familiar face in a growing number of amateur productions locally. In 1946, Sims first applied to RADA, but her audition was unsuccessful. Her first audition included a rendition of Winnie the Pooh. She did succeed in being admitted to PARADA, the academy’s preparatory school, and finally, on her fourth attempt, she graduated and was trained at RADA. She graduated from RADA in 1950 at the age of 19. One of her first stage performances was in the 1951 pantomime, The Happy Ha’penny, opposite Stanley Baxter at Glasgow’s Citizens Theatre. Sims appeared in a number of Brian Rix’s Aldwych Theatre farces, but revue was Sims’ greatest medium, especially in the works of Peter Myers. In 1958, she got a part in Peter Coke’s play Breath of Spring, which opened at the Cambridge Theatre in March, transferring to the Duke of York’s Theatre in August 1958, which ran until April 1959. Sims preferred film to stage work. “It was, of course, lovely to be in a successful play, to have the excitement of performing a hit to packed houses (and, not least, the assurance of a regular income for the foreseeable future). But, on the other hand, I found it extremely difficult to keep a performance fresh, and I’d soon get bored.”

Sims made her first film appearance in Will Any Gentleman? with George Cole in 1953, closely followed by Trouble in Store with Norman Wisdom. In 1954, she appeared as Miss Dawn in The Belles of St Trinian’s, and made a cameo appearance in Doctor in the House, opposite Dirk Bogarde as the sexually repressed Nurse Rigor Mortis. Sims became a regular in the Doctors series, which was produced by Betty E. Box, and was hence spotted by Box’s husband Peter Rogers. She had a small part in the 1957 film Carry on Admiral, unrelated to the later Carry On series and with no other cast members in common with the series. In 1958, Sims received a script from Peter Rogers; it was for Carry On Nurse. The film Carry On Sergeant had been a huge success at the box office and in the autumn of that year, Rogers and director Gerald Thomas began planning a follow-up. She first starred in Carry On Nurse, then Carry On Teacher, followed by Carry On Constable and Carry On Regardless, and this sealed her future as a regular Carry On performer. Following a bout of ill health, Dilys Laye had to be brought in to take her place in Carry On Cruising at very short notice; however, Sims rejoined the team with Carry On Cleo. Her role in this was to set the tone for the rest of the Carry On films. “…[F]or once the costumes were made for me, rather than my having to resort to some old dress that had been used before and had to have a new panel sewn in the back to accommodate my girth – which by now was unvaryingly plump.” Sims’ characters evolved from objects of desire in the early films to frumpy, nagging wives in the later ones, epitomised by the Emily Bung role in Carry On Screaming. Following the success of Carry On Cleo, she stayed with the films all the way though to the final one in the original series, Carry On Emmannuelle. Sims appeared in 24 Carry On films in all; she did not return for the one-off revival film, Carry On Columbus (1992). However, she did appear alongside Kenneth Williams in the radio show Stop Messing About in 1969–70. Prior to this she had worked on the BBC Radio comedy Play it Cool, with Hugh Paddick and Ian Carmichael.

After the Carry On series ended in 1978, Sims continued to work on television. She appeared opposite Katharine Hepburn and Laurence Olivier in the award-winning 1975 television film Love Among the Ruins and had a recurring role as Gran in the BBC comedy series Till Death Us Do Part. From 1979 until 1981, she played the recurring character Mrs Bloomsbury-Barton in Worzel Gummidge for Southern Television. During 1986 and 1987, Sims starred as Annie Begley alongside Angela Thorne in the Yorkshire Television sitcom Farrington of the F.O. Also in 1986, Sims appeared in the long-running BBC science fiction series Doctor Who in the four episodes of The Trial of a Time Lord: The Mysterious Planet as Katryca. She also played Miss Murgatroyd in the Miss Marple adaptation A Murder is Announced, Betsy Prig in a star-studded adaptation of Dickens’ Martin Chuzzlewit and Lady Fox-Custard in Simon and the Witch. In 1987 she joined the cast on And There’s More and was paired up with Nicholas Smith for a number of sketches for each episode as an old couple.

In 1989, she appeared as a medium in the video for Morrissey’s “Ouija Board, Ouija Board”. She played Mrs Wembley in the BBC comedy series On the Up, which starred Dennis Waterman and ran from 1990 to 1992. From 1994, she played Madge Hardcastle, stepmother of Geoffrey Palmer’s character Lionel in As Time Goes By. Sims also appeared in episodes of the hit television comedy series Only Fools and Horses and The Goodies, in the One Foot in the Grave special One Foot in the Algarve, and made a guest appearance in a sketch show with Victoria Wood. In her later years, Sims fought a long battle against depression. This was worsened by the deaths of her agent Peter Eade, her best friend Hattie Jacques and her mother, all within a two-year period, after which she fell into alcoholism. Sims suffered from Bell’s palsy in 1999 and fractured her hip in 2000, but recovered well. However, her alcoholism was beginning to dominate life in her rented Kensington flat, and she described herself as “the queen of puddings.” After assessment by a doctor, she was offered a place in a rehabilitation centre, but declined. Offered the opportunity to write her autobiography, she took a role in the BBC television film The Last of the Blonde Bombshells, alongside Dame Judi Dench and Olympia Dukakis.

Sims entered hospital in November 2000, and complications of a routine operation caused her to slip into a coma. Her lifelong friend and stand-in Norah Holland spoke of the doctors’ amazement at her strength and courage throughout her final illness. On 27 June 2001, ten minutes before she died, Norah Holland spoke to her gently about Kenneth Williams, Hattie Jacques and their time on the Carry On films. She died with Holland holding her hand. She was cremated at Putney Vale Crematorium, and her ashes scattered in the grounds there.