A Squadron of the Blue heading down the Channel off the Downs

Pocock was the son of Nicholas Pocock (c.1705-1759), a Bristol seaman, and Mary Innes, who was related to the Duke of Roxburgh. By 1766, Pocock was in command of the Lloyd, a merchant ship belonging to Richard Champion, a prominent Bristol merchant and maker of Bristol porcelain. He was subsequently captain of Champion's ships Betsey and Minerva. Pocock made at least twelve voyages to America, as well as trips to the West Indian islands of Dominica, St. Kitts and Nevis, and the Mediterranean. In 1794, he was present at the battle of the Glorious First of June onboard H.M.S. Pegasus with Lord Howe's fleet. Pocock kept detailed logbooks during these voyages, illustrated with meticulous pen and ink and wash drawings which he extensively annotated. His twenty years of experience as a merchant seaman stood him in good stead as a marine artist, although he did not seriously take up painting until about 1778. In 1780, he married Anne Evans (1752-1827), with whom he had nine children, including the artist William Innes Pocock.

In 1789, Pocock moved to London with his family and established his reputation as a successful marine painter. He received numerous commissions to depict the naval engagements and battles of the period and took painstaking care in obtaining first-hand information from those who had participated, which included correspondence, sketches and diagrams. His patrons included Admiral Lord Hood and his brother, Lord Bridport, and First Lord of the Admiralty, Lord Barham.