Thompson attended Trinity Academy, Halifax, and Hipperholme Grammar School. Following National Service he ran a farm near Halifax then joined the family butcher business of his father, Geoff Thompson, known for its black puddings. His mother, Rachel, had worked as a weaver from the age of 12 until her marriage. Thompson expanded the business considerably and also developed a successful plastics manufacturing business.
Thompson became involved in politics at a young age, setting up Halifax Young Conservatives. He became a county councillor for the West Riding from 1967, joining the new West Yorkshire county council in 1974, then Calderdale district council from 1975 until 1979. He first stood for Parliament at the 1970 general election for the safe Labour seat of Batley and Morley. He stood in the marginal seat of Sowerby in both the February 1974 and October 1974 elections, losing by small margins. In the 1979 election he stood again in Sowerby, beating Max Madden by 1,180. At the 1983 general election, the seat was adjusted and renamed Calder Valley.
Thompson was known as a solid, stout, no-nonsense Yorkshireman. He worked his way up through the whips office before joining the Ministry of Agriculture, Fisheries and Food as a junior minister. He was sacked in 1989 but bore no resentment against Margaret Thatcher, telling his colleagues: "There is no iceberg here, but a shire horse unharnessed and put out to grass on blue Conservative grass."
At the last Prime Minister's Questions given by Margaret Thatcher in November 1990 he famously said that if the Prime Minister visited his constituency, she would find scores of people telling her what they had told him, that she "was a good 'un."
In July 1997, following the loss of his seat in parliament, Thompson was appointed Director of the War Memorials Trust (then known as The Friends of War Memorials), a charity which he had helped to found in 1996. He held the post until his death in 2005, aged 73.