Frank Thornton Ball was born in Dulwich, London, the son of Rosina Mary (née Thornton) and William Ernest Ball. His father was an organist at St Stephen's Church, Dulwich, where Frank learned to play the organ for a short while. Music proved too difficult for him, however, and he wanted to act from an early age. His father, who worked in a bank, wanted him to get a "proper" job, so he began working in insurance after leaving Alleyn's School. He soon enrolled at a small acting school, the London School of Dramatic Art, and took evening classes. After two years working at the insurance company he was invited to become a day student at the acting school and persuaded his father to finance his studies.
During the Second World War, Thornton was evacuated along with the drama school, and his first job was touring with four plays in Ireland, beginning in County Tipperary. After that he served as an airman in the Royal Air Force before ending the war as an officer. From the rank of leading aircraftman he was commissioned as a pilot officer on probation (emergency) on 1 December 1944. On 1 June 1945 his commission was confirmed and he was promoted to flying officer (war substantive). He was demobilised in 1947.
On 5 June 1945, Thornton married actress Beryl Evans in West Wickham; the couple had a daughter, Jane.
Almost immediately after demobilisation, Thornton joined a repertory company. His first credited screen role was in the film Radio Cab Murder (1954). After working on stage and in a few films during the 1950s, he became a familiar face on British television, specialising in comedy. He was a regular on It's a Square World, and appeared in classic British sitcoms such as Hancock ("The Blood Donor", 1961), Sykes, The Goodies and Love Thy Neighbour. He appeared in the Danger Man episode "The Assassin" as Pepe in 1961, and as a tailor in The Sentimental Agent episode 'Scroll of Islam' (1963). He appeared with Dick Emery, Benny Hill, Frankie Howerd, Harry Worth, Reg Varney and Spike Milligan in their comedy shows. He appeared in five episodes of Steptoe and Son during its original run from 1962 to 1965, and in 1973 appeared in the film Steptoe and Son Ride Again and that year's television Christmas special, the most recurring actor in the series aside from Wilfrid Brambell and Harry H. Corbett.
From 1966 to 1968 he starred in the BBC radio comedy The Embassy Lark, a spin-off of The Navy Lark. He appeared in at least one episode of The Navy Lark as CPO Nathanial Pertwee, filling in for Jon Pertwee who was indisposed. He also appeared in at least one episode of The Navy Lark as his character from The Embassy Lark. In 1969, he starred in The Big Business Lark which ran for one season of thirteen episodes. This was not strictly a spin-off from The Navy Lark, other than being another "Lark" written by Laurie Wyman. He continued to appear in films, mostly comedies, during the 1960s and 1970s, including Carry On Screaming!, alongside Steptoe and Son star Harry H. Corbett, The Early Bird, The Bed Sitting Room, Up the Chastity Belt, Some Will, Some Won't, "A Funny Thing Happened on the Way to the Forum" and No Sex Please, We're British, as well as television sitcom spin-offs. He appeared in The Private Life of Sherlock Holmes (1970) as the one-armed doorman for the Diogenes Club. In 1974, he made a rare dramatic appearance as Prince Albert in the second episode of Fall of Eagles.
Thornton was best known for playing Captain Peacock in the long-running BBC comedy series Are You Being Served? from 1972 to 1985. He reprised his role for Grace & Favour from 1992 to 1993. In 1984 he starred as Sir John Treymane in the hit London musical Me and My Girl, earning rave reviews and an Olivier Award nomination. He also guest-starred in an episode of the BBC Radio series of Dad's Army entitled "Ten Seconds from Now" as the BBC producer Willoughby Maxwell-Troughton, who has to coordinate the chaotic platoon as it tries to broadcast to the nation in a morale-boosting Gang Show-style extravaganza. In 1980 he joined John Cleese in the BBC Television Shakespeare production of The Taming of the Shrew.
At some point in the 1990s he appeared as The Major-General (Stanley) in a production of The Pirates Of Penzance at the London Palladium which starred Paul Nicholas as the Pirate King and Bonnie Langford.
In 1997 he took the role of Herbert "Truly" Truelove in Last of the Summer Wine, replacing Brian Wilde, who had suggested him for the role. He can also be seen in the film Gosford Park (2001) as Mr Burkett. Thornton was the subject of This Is Your Life in 1998, when he was surprised by Michael Aspel at Pinewood Studios.
Thornton died from natural causes peacefully in his sleep at his home in Barnes, London, on 16 March 2013, aged 92.