Thompson was born in London, and attended Highgate School, before reading History at Brasenose College, Oxford where he edited the university newspaper, Cherwell. He lived with his father, Gordon Thompson and his late mother Brenda. Thompson was an only child.

Early in his career Thompson produced the radio comedy programmes The News Quiz and The Mary Whitehouse Experience. Following his move into television, he produced Newman and Baddiel in Pieces, Harry Enfield and Chums and Monkey Dust, and co-produced Never Mind The Buzzcocks. In 1998 he was part of BBC Radio 4's 5-part political satire programme Cartoons, Lampoons, and Buffoons.

Harry Thompson also produced non-comedy documentaries for BBC Radio. He made several programmes with writer/presenter Terence Pettigrew, starting with anniversary tributes to Hollywood icons James Dean (You're Tearing Me Apart) and Montgomery Clift (I Had The Misery Thursday). Pettigrew and Thompson subsequently worked together on a second series of documentaries, including on national service Caught In The Draft, and also about the evacuation of children from major British cities during World War II (Nobody Cried When The Trains Pulled Out). Both programmes were presented by Michael Aspel.

Afterwards, Pettigrew said, "I was a new to broadcasting in those days, and I found Harry to be inventive and tireless and wonderfully patient. I couldn't have had a better teacher. This was before his great television triumphs and awards, all of which were richly deserved."

He was best known for producing the BBC panel shows Have I Got News For You and They Think It's All Over, producing the latter for the first eight years of its run.

He was instrumental in the creation of the comic character Ali G for The 11 O'Clock Show, and as a comedy writer his credits included Da Ali G Show.

During these productions he was able to gain exposure for a very large proportion of those who went on to become prominent figures in contemporary British comedy, including: Sacha Baron Cohen, Angus Deayton, Harry Enfield, Ricky Gervais, Nick Hancock, Ian Hislop, Mark Lamarr, Paul Merton and Paul Whitehouse.

In 2003, The Observer listed him as one of the 50 funniest or most influential people in British comedy. In December 2005 he was to have received the Jury's Award for Outstanding Contribution to British Comedy at the British Comedy Awards but died before receiving it.

His last broadcast work was the Channel 5 sitcom Respectable, set in a suburban brothel.

In a 2005 episode of Have I Got News For You, featuring Alexander Armstrong as host and panelists Fi Glover and Ian McMillan, a message stating "In Memory of Harry Thompson, the first producer of Have I Got News For You (1960 - 2005)" was displayed.

Thompson wrote biographies of Peter Cook, Richard Ingrams and Tintin creator Hergé.

In June 2005, Thompson's only novel, entitled This Thing Of Darkness (a historical novel chronicling the life of Robert Fitzroy - later published in the United States as To The Edge Of The World), was published and long-listed for the Booker prize.

He also wrote Penguins Stopped Play, an account of the attempt by his beloved cricket team, The Captain Scott Invitation XI, to tour all seven continents of the world.

He was diagnosed with inoperable (stage III) lung cancer in April 2005, despite never having smoked, and died, aged 45, on November 7 the same year, in the Royal Borough of Kensington and Chelsea, London. He married his girlfriend, Lisa Whadcock, on the day of his death, in the same borough. Mr Thompson died intestate in 2005 and the regulations mean his widow Lisa inherited only £125,000 of his £1million estate.The rest of his fortune has been split in two, with one half going to his two children, Bill, and Betty.Mrs Thompson, 34, has access only to the interest on the remaining half, which will go to his children on her death

He is survived by his two children from his first marriage (Betty 1994 and William 1996) to Fiona Duff (1993—98) who live in Edinburgh.