Brenton was born in British America but his family relocated to England after the outbreak of the American War of Independence. He followed his father into the Royal Navy, enrolling as a midshipman and reached the rank of lieutenant in 1790. After accepting a commission to serve in the Royal Swedish Navy during the Russo-Swedish War, Brenton returned to the Royal Navy and was given his first command, HMS "Trepassey", in 1791. Serving in the Mediterranean during the French Revolutionary Wars, Brenton took part in the Battle of Cape St Vincent on HMS "Barfleur" and earned the patronage of Admiral Sir John Jervis. He was subsequently appointed commander of HMS "Speedy" in which he distinguished himself in a number actions against Spanish ships. He was promoted to post-captain in 1800 and served as flag captain on HMS "Caesar" under Rear Admiral Sir James Samuarez, taking part in the First and Second Battles of Algeciras.