Eyles was the son of Thomas Eyles of Stratton Audley, Oxfordshire, and his wife, Ann Woodward Baxter, and, in turn, the father of Major Thomas Woodward Eyles. Little is recorded about Eyles's early life and career in the navy. He was a protégé of Sir John Borlase Warren and was serving aboard Warren's ship, the 44-gun , during the Quiberon Expedition in mid-1795. Eyles was a lieutenant at this time, and did not have an active posting, but Warren lobbied the Admiralty to give Eyles a position on the expedition, and himself appointed Eyles to oversee all matters related to signalling and transportation. Encouraged by the expedition's initial success, the Admiralty promoted Eyles to post-captain on 13 July 1795 and Warren to commodore. Eyles received an appointment to command the "Pomone", initially as acting captain, and later being confirmed as captain. The expedition ultimately ended in the frustration of the British plans to encourage a French Royalist rising, but Eyles and Warren both benefited from it.