Thaw came from a working class background, having been born in Longsight, Manchester to parents John and Dorothy. He studied at the Royal Academy of Dramatic Art where he was a contemporary of Tom Courtenay.
On leaving RADA, Thaw was awarded a contract with the Liverpool Playhouse. His first film role was a bit part in the 1962 adaptation of The Loneliness of the Long Distance Runner starring Tom Courtenay; and he also guested in an early episode of The Avengers.
Thaw will perhaps be best remembered for two roles: the hard-bitten Flying Squad detective Jack Regan in the television series (and two films) The Sweeney (1975 – 1978), which established him as a major star in the United Kingdom, and as the quietly-spoken, introspective and bitter detective Inspector Morse (1987 – 2001), with specials in 1995 – 1998 and 2000.
He won two BAFTA awards for Inspector Morse.
He subsequently played liberal barrister James Kavanagh in Kavanagh QC (1995 – 1999), with a special in 2001. Thaw also tried his hand at comedy with his own sitcom called Home to Roost (1985 – 1988).
His only screen projects not considered a popular success were the BBC series A Year in Provence and the LWT series Mitch, in which he played a journalist..
Thaw appeared in a number of films, including Cry Freedom, for which he received a BAFTA nomination for Best Supporting Actor, and Chaplin for director Richard Attenborough.
In 1964 Thaw married Sally Alexander, but they divorced four years later. He married actress Sheila Hancock in 1973 and remained with her until his death from cancer in 2002, aged 60.
Thaw had two daughters: Abigail Thaw from his first marriage, and Joanna Thaw from his second.
In her 2004 autobiography Sheila Hancock revealed the extent of Thaw's alcoholism that had started in the late 1970s and caused problems in their marriage and the gaps in Thaw's career in the early 1980s and later 1990s. Thaw was eventually able to get his alcoholism under control a year before his death.
Thaw was awarded the CBE in 1994.