Heddington was a midshipman on the armed tender Chatham which, with Vancouver's Discovery, set sail from Falmouth on 1 April 1791 under instructions from the Admiralty to survey the northwest coast of America. Sailing via the Cape, New Holland, New Zealand, the south Pacific and Hawaii, they reached the northwest coast and surveyed the coastline until September 1794, the Chatham returning to England in October 1795. Heddington was one of three seamen (along with Henry Humphreys and John Sykes) whose drawings were later worked up by William Alexander to illustrate the voyage, Heddington's drawing here the model for plate IV in volume I of Vancouver's Voyage. Heddington prepared several surveys and drawings of the coast between Cape Elizabeth and Prince William Sound. After the voyage, Heddington submitted his work to the Hydrographic Office, but later in 1808 requested that his work be returned. The Admiralty honoured the request only to lose all record or trace of the drawings. Humphreys' and Sykes's drawings remain in the Hydrographic Office, Taunton and there are further voyage drawings by the latter in the Bancroft Library (U.C. Berkeley, Honeyman collection), California.
Bute Inlet, named for Charles Stuart, grandson of the 3rd Earl of Bute and master's mate on Vancouver's Discovery, is an inlet on the British Columbia coast.