Bolam was born in Sunderland, County Durham, England. His father, Robert Alfred Bolam, was from Northumberland, and his mother, Marion Alice Drury, from County Durham.
After attending Bede Grammar School, Sunderland, Bolam attended Bemrose School in Derby. He was formally trained at the Central School of Speech and Drama in London, and first appeared on screens in the early 1960s, initially in popular TV shows such as Z-Cars and the gritty northern films A Kind of Loving and The Loneliness of the Long Distance Runner. He appeared along with John Thaw in the 1967 Granada TV serial, Inheritance.
The Likely Lads made Bolam a star during its 1964 to 1966 run. Bolam himself adapted the shows for BBC radio soon afterwards, and appeared in films such as Half a Sixpence, Otley, and O Lucky Man! before the "Lads" returned in 1973. Whatever Happened to the Likely Lads? ran for two series, in 1973 and 1974 and a 45-minute Christmas special broadcast on Christmas Eve 1974.
In 1975 Bolam appeared alongside the original cast in a further BBC Radio series adapted from the 1973 TV series and in 1976 there was a further reunion in a feature film spin-off from the series, simply entitled The Likely Lads. Bolam's co-star Rodney Bewes revealed in 2005 that the two actors had not spoken since the film had been made, a period of over thirty years. The rift, according to Bewes, developed through his indiscreetly telling a journalist that when Bolam's wife revealed she was pregnant, Bolam was so startled that the car he was driving mounted a pavement and almost crashed into a lamp post.
Bolam has never commented on what caused the rift, but is known for being guarded about his private life. He once remarked: "I'm having a man fix the track rods on my car. I don't want to know anything about him. Why should he want to know anything about me?"
In 1976 Bolam made a return to straight drama, as Jack Ford in the BBC Television series When the Boat Comes In, which ran until 1981. Since then he has mostly appeared in comedies and comedy dramas, including Only When I Laugh (as Roy Figgis) from 29 October 1979 to 16 December 1982, The Beiderbecke Affair (as Trevor Chaplin) in 1985, The Beiderbecke Tapes in 1987, Andy Capp (in the title role), The Beiderbecke Connection in 1988, Second Thoughts (as Bill MacGregor) from 3 May 1991 to 14 October 1994, Midsomer Murders, Pay and Display, Dalziel and Pascoe, Close and True, Born and Bred (as Dr Arthur Gilder), and New Tricks (as Jack Halford). Another memorable role was alongside Timothy West and Sheila Hancock in the 2002 series of the BBC drama Bedtime, in which Bolam played the seemingly decent but actually crooked Ronnie Stribling.
On radio, in 1978 he played Willie Garvin in a BBC World Service radio adaptation of the Modesty Blaise book Last Day in Limbo. In 1982 he provided the voice for The Tod in the animated film version of The Plague Dogs. In the mid-1980s he co-starred in the original radio version of the romantic sitcom Second Thoughts, which ran for several series and was subsequently adapted for television. In the year 2000 he played Sir Archibald Flint in the Doctor Who audio play The Spectre of Lanyon Moor. He was also the narrator for the three-part football documentary Three Lions, which aired before Euro 2000 on BBC One. The three episodes were about England National Team's history from the 1966 World Cup until before the Euro 2000 finals.
In 2002 he played the serial killer Harold Shipman, in Shipman, the ITV adaptation of Brian Masters' book on the case, Prescription for Murder and Father Leonard Tibbings in Dalziel and Pascoe (Ser. 7, Ep. 1 'Sins of the Fathers'). He portrayed Harold Wilson, the former Prime Minister, in the 2006 BBC documentary The Plot Against Harold Wilson. He appeared in Frank Loesser's musical How to Succeed in Business Without Really Trying at the Chichester Festival Theatre during the 2005 summer season. He is currently playing Grandpa in the Cbeebies show Grandpa in My Pocket as the Grandpa with a magic hat, which when he put on, he was able to shrink. In 2009 he played Ken Lewis, CEO of the Bank of America, in the television dramatisation The Last Days of Lehman Brothers.
His appearances on the London stage include Jeffrey Bernard is Unwell by Keith Waterhouse and Ben Elton´s play, Gasping. In 1974, he appeared in a novel production of 'Macbeth' at The Young Vic, in which the lead role was shared by Bolam and two other actors. Bolam was appointed Member of the Order of the British Empire (MBE) in the 2009 Birthday Honours. It was announced on 20 September 2011, that Bolam had quit the role of Jack Halford in New Tricks, just days after two more series were commissioned.
Bolam continues to work in the theatre as well as on television. During spring 2015 he appeared in the play "Bomber's Moon" by William Ivory at the Park Theatre, Finsbury Park, London.
Bolam lives in Wisborough Green near Billingshurst, West Sussex and Chiswick, London, with his wife, the actress Susan Jameson (who co-starred with him in the TV series When the Boat Comes In, New Tricks, Close and True and Grandpa in My Pocket). They have a daughter, Lucy, and two grandchildren.
Bolam has appeared in a video protesting against oil drilling near the village of Wisborough Green in West Sussex.
Bolam was appointed Member of the Order of the British Empire (MBE) in the 2009 Birthday Honours.
Prior to becoming an actor, Bolam trained as a chartered accountant.The Kitchen as Michael (1961)
A Kind of Loving as Jeff (1962)
H.M.S. Defiant as Midshipman Assisting in Operation (1962)
The Loneliness of the Long Distance Runner as Mike (1962)
Murder Most Foul as Bill Hanson (1964)
Otley as Albert (1968)
Crucible of Terror as John 'Jack' Davies (1971)
Straight on till Morning as Joey (1972)
O Lucky Man! as Attenborough / Examination Doctor (1973)
In Celebration as Colin (1975)
The Likely Lads as Terry Collier (1976)
The Plague Dogs as The Tod (voice only) (1982)
Clash of Loyalties as A. T. Wilson (1983)
Seaview Nights as Merlin (1994)
Clockwork Mice as Wackey (1996)
Stella Does Tricks as Mr. Peters (1996)
The Barber (1997)
The Island on Bird Street as Doctor Studjinsky (1997)
The End of the Affair as Mr. Savage (1999)
It Was an Accident as Vernon Fitch (2000)
To Kill a King as Denzil Holles (2003)