Thaw came from a working class background, having been born in Gorton, Manchester, to parents John and Dorothy (née Ablott). His father was a long distance lorry driver. He had a difficult childhood as his mother left him when he was seven years old and he didn't see her again until twelve years later. He had a younger brother called Ray. He grew up in the Burnage area of the city and attended Ducie Technical High School for Boys in Manchester. He entered the Royal Academy of Dramatic Art at the age of 17, where he was a contemporary of Tom Courtenay.

Soon after leaving RADA he made his stage début in A Shred of Evidence at the Liverpool Playhouse and was awarded a contract with the theatre. 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 acted on-stage opposite Sir Laurence Olivier in Semi-Detached (1962). He appeared in several episodes of the seminal BBC police series Z Cars in 1963–64 as a detective constable with a drink problem. Between 1964–66 he appeared as the central role of hard-nosed military policeman, Sgt John Mann, in two series of the ABC Weekend Television/ITV production Redcap. He was also a guest star in an early episode of The Avengers. In 1967 he appeared in the Granada TV/ITV series, Inheritance, alongside James Bolam and Michael Goodliffe, as well as appearing in TV plays such as The Talking Head and episodes of series such as Budgie, where he played against type (opposite Adam Faith) as an effeminate failed playwright with a full beard and a Welsh accent.

Thaw will perhaps be best remembered for two roles: the hard-bitten Flying Squad detective Jack Regan in the Thames Television/ITV series (and two films) The Sweeney (1974 – 1978), which established him as a major star in the United Kingdom, and as the quietly-spoken, introspective, well-educated and bitter detective Inspector Morse (1987 – 1993, with specials from 1995 – 1998 and 2000). Starring alongside Kevin Whately as the put upon Detective Sergeant Lewis, Morse became a cult character - "a cognitive curmudgeon with his love of classical music, his vintage Jaguar and spates of melancholy". Morse became one of the UK's most loved TV series - the final three episodes, shown in 2000, were seen by 18 million people - about one third of the British population. He won "Most Popular Actor" at the 1999 National Television Awards and won two BAFTA awards for his role as Morse.

He subsequently played liberal working class Lancastrian barrister James Kavanagh in Kavanagh QC (1995 – 1999, and a special in 2001). Thaw also tried his hand at comedy with two sitcoms — Thick as Thieves (London Weekend/ITV, 1974) with Bob Hoskins and Home to Roost (Yorkshire/ITV, 1985 – 1990). Thaw is best known in America for the Morse series, as well as the BBC series A Year in Provence with Lindsay Duncan.

During the 1970s and 1980s, Thaw frequently appeared in productions with the Royal Shakespeare Company and Royal National Theatre. He appeared in a number of films, including Cry Freedom, where he portrayed the conservative South African justice minister Jimmy Kruger, for which he received a BAFTA nomination for Best Supporting Actor, and Chaplin alongside Robert Downey Jr. for director Richard Attenborough.

Thaw also appeared in the TV adaptation of the Michelle Magorian book Goodnight Mister Tom (Carlton Television/ITV) as the title character. It won "Most Popular Drama" at the National Television Awards (1999). In September 2006, Thaw was voted by the general public as number 3 in a poll of TV's Greatest Stars.

In 1964, Thaw married Sally Alexander (a theater stage manager), but they divorced four years later.

He met actress Sheila Hancock in 1969 on the set of a London comedy So What About Love?. She was married to fellow actor Alexander "Alec" Ross, and after Thaw professed his love to Hancock, she told him that she would not have an affair. After the death of her husband (also from oesophageal cancer) in 1971, Thaw and Hancock got married on 24 December 1973 in Cirencester, and he remained with her until his death in 2002.

Thaw had three daughters (all of whom are actors): Abigail "Abs" Thaw from his first marriage, Joanna "Jo" Thaw from his second, and he also adopted Sheila Hancock's daughter Melanie Jane "Ellie" from her first marriage. Melanie legally changed her name from Ross to Thaw.

Thaw was a lifelong supporter of the Labour Party.