Sir Matthew William Thompson Bt (1 February 1820 – 1 December 1891) was a British railway director and Liberal Party politician.
Almost immediately he began to take an active share in the conduct of municipal affairs, becoming a town councillor in 1858, an alderman in 1860, and mayor of Bradford in 1862.
In 1865 he was elected a director of the Midland Railway, and in 1867 was returned as a liberal-conservative borough MP for Bradford, with William Edward Forster as his colleague.
He was not an ardent politician, and did not stand at the general election in 1868; but on the unseating of the conservative member, Henry William Ripley, in March 1869, he again contested the constituency, but was defeated.
The sanction of parliament for the erection of the Forth Bridge had been obtained in 1873, but the work was not begun till 1882, and the direction of the policy of the Midland Railway company was greatly influenced by Thompson.