Inman was born in 1935 in Preston, Lancashire, and was often said to be a cousin of Actress Josephine Tewson, though she has denied they are related. (They did, however, play half-siblings in the 1977 sitcom Odd Man Out.) At the age of 12, Inman moved with his parents to Blackpool where his mother ran a boarding house, while his father owned a hairdressing Business. As a child, he enjoyed dressmaking. He was educated at Claridge House in Preston, and then a secondary modern. Inman always wanted to be an actor, and his parents paid for him to have elocution lessons at the local church hall. At the age of 13 he made his stage debut in the Pavilion on Blackpool's South Pier, in a melodrama entitled Freda. Aged 15, he took a job at the pier, making tea, clearing up and playing parts in plays.

Inman made his West End debut in the 1960s when he appeared in Ann Veronica at the Cambridge Theatre. He also played in Salad Days at the Windmill Theatre in 1975, and as Lord Fancourt Babberley in Charley's Aunt at the Adelphi Theatre in 1979. He also played in many summer shows, and established himself as a dame in pantomime, appearing regularly as one of the two ugly sisters alongside Comedian Barry Howard. His other stage appearances included his own show Fancy Free and Pyjama Tops, My Fat Friend and Bedside Manners.

Inman made his television debut in the sitcom A Slight Case Of... in 1965, then in 1966 he appeared in two episodes of the BBC sitcom Hugh and I then in 1970 he appeared in one episode of the ITV sitcom Two in Clover. In 1972, he was asked by David Croft to play a part in a Comedy Playhouse pilot called Are You Being Served?. This was a sitcom set in a department store, written by Croft with Jeremy Lloyd, and based on the latter's experiences working at Simpsons of Piccadilly. Playing a minor role with only a few lines, he was soon asked to "camp it up", despite initial reluctance from the BBC to include such a camp character. The pilot was broadcast in September 1972. The broadcast was followed by the five episodes of the first series in early 1973. The first series showing opposite Coronation Street on ITV attracted little attention, but repeats later that year were very successful.

During the 69-episode, 13-year run of Are You Being Served?, Inman also appeared in the 1977 film of the series, in which the characters visited the fictional Spanish holiday resort of "Costa Plonka". Odd Man Out (1977), his own sitcom, Inman played the owner of a fish and chip shop who inherits half of a rock factory; and Take a Letter, Mr. Jones (1981), a sitcom in which Inman played Graham Jones, who is secretary to Rula Lenska's character Joan Warner. Inman also toured with his own shows, and he released several records, including "Are You Being Served, Sir?", which reached number 39 in the UK singles charts. This came from an LP of the same name, and was followed by two further albums: I'm Free in 1977 and With a Bit of Brass in 1978, the first two issued by DJM Records.

From 1980 to 1981, Inman also played Mr Humphries in the Australian version of Are You Being Served?, the only cast member of the original Are You Being Served? series to do so. He made many appearances on BBC TV's long running television show, The Good Old Days.

Are You Being Served? ran for 10 series until 1985. At its height, in the mid to late 1970s, it regularly attracted British audiences of up to 22 million viewers. Inman's portrayal of Mr Humphries won him the BBC TV Personality of the Year in 1976 and he was voted the funniest man on television by TV Times readers. The series also became popular in the United States, where Inman became a gay cultural icon. Once, in San Francisco, a passing Cyclist spotted Inman and fell off his bicycle in surprise, crying "Mr Humphries, I love you!"

He made a cameo appearance in the film The Tall Guy (1989), and was one of five of the Are You Being Served? cast to be reunited in character for the sitcom Grace & Favour (titled Are You Being Served? Again! in the United States), which ran for twelve episodes in 1992 and 1993. Inman had a small part as Lady Capulet in the film Shakespeare in Love (1998) and appeared in the 1999 French and Saunders Christmas special. He appeared as Father Chinwag in the film The Mumbo Jumbo (2000).

Inman suffered from poor health in his later years. He was hospitalised with bronchitis in 1993, and collapsed on stage in 1995. He was admitted to Paddington's St Mary's Hospital in 2001 after suffering breathing difficulties and spent three days in intensive care.

After the end of Are You Being Served?, Inman became one of the nation's best known pantomime dames and appeared in over 40 pantomimes across the United Kingdom. He also toured Australia, starring in a number of productions including Bedside Manners (2003) and a revival of Are You Being Served? (2001) as a stage show at Twelfth Night Theatre, Brisbane. In 2004, Inman made additional television appearances in Doctors and Revolver.

In December 2004, Inman was forced to cancel an appearance in a pantomime as he was reportedly suffering from a hepatitis A infection, allegedly contracted from contaminated food. Following this, he never worked again and it was claimed that he suffered complications from this infection for the rest of his life.

He lived in a mews house in Little Venice for 30 years. On 23 December 2005, Inman entered into a civil partnership at Westminster Register Office with his partner of 33 years (at the time), Ron Lynch.

It was reported in July 2007 that Inman had left nearly his entire estate, including more than £2.8m, to his civil partner Ron Lynch. The only other portion of his estate given to another, was a £5,000 bequest to the Entertainment Artistes Benevolent Fund. The Daily Mail newspaper said at the time that Inman's "estate is believed to be the highest profile will of a gay man in a civil partnership since the ceremonies became legal in 2005".