Dawson was married to his first wife, Margaret, from 25 June 1960 until her death on 15 April 1986 from cancer. They had three children: Julie, Pamela and Stuart. He married his second wife, Tracy, on 6 May 1989; she was 17 years younger. They had a daughter, Charlotte, who was born on 3 October 1992.

Dawson claimed in his autobiography that he began entertaining as a Pianist in a Parisian brothel. Making a living as a Pianist evolved into comedy when he got laughs by playing wrong notes and complaining to the audience. He made his television debut on the talent show Opportunity Knocks in 1967 and became a prominent comic on British television for the rest of his life.

Dawson starred in Listen to Les on BBC Radio 2 in the 1970s and 1980s. Television series in which he appeared included Sez Les for Yorkshire Television, The Dawson Watch for the BBC, written by Andy Hamilton and Terry Ravenscroft, The Les Dawson Show, written by Terry Ravenscroft, Dawson's Weekly, Jokers Wild (1969–73) and the quiz show Blankety Blank, which he presented from 1984 until its cancellation in 1990. He made many appearances on BBC Television's variety show, The Good Old Days in the 1970s and 80s. When Richard Wilson turned down the part of Victor Meldrew in the BBC sitcom One Foot In The Grave, Writer David Renwick considered Dawson for the role, but Wilson changed his mind before it was offered. His final TV appearance was on the LWT series Surprise, Surprise hosted by Cilla Black, in which he sang a comic rendition of "I Got You Babe" with a woman from the audience who wanted to sing with him. The episode was aired shortly after his death.

Dawson was the subject of This Is Your Life on two occasions, in December 1971 when Eamonn Andrews surprised him on Opportunity Knocks, and again 21 years later, in what would be one of his last television appearances, when he was surprised by Michael Aspel on stage at the Theatre Royal, Plymouth, at the curtain call of the pantomime Dick Whittington in December 1992.

Dawson nearly died in 1985 from a failing prostate gland, complicated by blood poisoning.

On 10 June 1993, Dawson went to a hospital in Whalley Range, Manchester, for a medical check-up. While waiting for the results with his wife, he suffered a major heart attack and died.

In the Comedians' Comedian, a three-hour programme on UK's Channel 4 on 1 January 2005. Dawson was 37th in the top 50 comedians of all time, voted by fellow comedians and Business insiders.

On 23 October 2008, 15 years after his death, a bronze statue by Graham Ibbeson was unveiled by his widow Tracy and daughter Charlotte in the ornamental gardens next to the pier in St Anne's-on-Sea, Lancashire, where Dawson lived for many years.

The BBC broadcast, on BBC Two, The Many Faces of Les Dawson, a retrospective, on Christmas Eve 2011.

On 1 June 2013 ITV broadcast Les Dawson: An Audience with That Never Was. The programme featured a Pepper's ghost projection of Dawson, presenting content for a 1993 edition of An Audience with... to be hosted by Dawson but unused due to his death two weeks before recording. The show served as a tribute and featured celebrities including Bruce Forsyth, Cilla Black, Terry Wogan and Ken Dodd. Also among the audience were Dawson's wife Tracy and daughter Charlotte (who was only eight months old when he died).

On 10 February 2014, the BBC reported that Dawson's daughter Charlotte had found a 110-page "unpublished story of love and mystery, titled An Echo of Shadows, [that] was written under the name Maria Brett-Cooper...".

Before his fame Dawson wrote poetry and kept it secret. It was not expected that someone of his working-class background would have literary ambitions. In a BBC Television documentary, he spoke of his love for canonical figures in English literature, in particular the 19th century Essayist Charles Lamb, whose florid style influenced Dawson's.