Thompson was educated at boarding school in Yorkshire and grammar school in West London, before spending two years at art school in Ealing and Hammersmith. He studied ceramics and worked as a silk screen painter and graphic designer. He then studied film making for a year and worked for the BBC creating documentaries. In the late 1960s Thompson moved to the Outer Hebrides islands off Scotland and then moved to Cumbria in 1975 where he specialised in ceramics.
Thompson started writing and illustrating children's books in 1990 . His first two books, Ethel the Chicken and A Giant Called Norman Mary were illustrated in black and white and published in 1991 by Hodder & Stoughton. His first picture book was The Paperbag Prince, published by Julia MacRae in 1992. In 1993 Random House published Looking for Atlantis, the first of his picture books with elaborate visual details.
In 1994, when an Australian teacher-librarian read this book to a Year 7 class of boys, they asked if Thompson could visit their school and raised funds towards the cost of his flight. Thompson subsequently settled near Coffs Harbour, later becoming an Australian citizen.
Until 2002 Thompson's illustrations were on hard surfaced line board, rather than paper. The board allowed Thompson to develop a technique where he could lift colour off and work over an illustration again and again without the surface breaking up. Since 2002 he has been illustrating his books by computer.