Thompson was born in Barham, Kent on 28 February 1766. His uncle, through his mother, was Commodore Edward Thompson, and it was through this relative's influence that Thomas joined the navy in June 1778, when Edward was appointed to command the sloop . He served on the "Hyaena" with his uncle, spending most of the time in the waters off the British Isles, before accompanying Rodney's fleet to the Relief of Gibraltar in January 1780. The "Hyaena" was later entrusted with carrying copies of Rodney's despatches.