Thompson was educated at Eton College, and on 20 December 1845 received the commission of ensign in the East Indian Company's army.
In 1854 he volunteered in the Turkish Army, received the rank of major, and, after visiting the Crimea, proceeded to Kars, where he arrived in March 1855.
His bravery won the admiration of the besiegers, and, on the surrender of Kars in November, Nikolay Muravyov-Karsky, the Russian commander, returned him his sword.
On 9 November he was appointed captain unattached in the British Army; on 7 February 1856 he received the third class of the Turkish Order of the Medjidie; and on 10 May was nominated an honorary CB.
He died unmarried at 70 Gloucester Street, Belgrave Road, on 13 June 1856, immediately after his return from Russia, where he had been detained a prisoner of war.