Born the son of the Hon. Edward Russell, a younger son of the 4th Earl of Bedford and Penelope Russell (née Hill), daughter of Sir Moyses Hill of Hillsborough, County Down and widow of Sir William Brooke, Russell briefly attended St John's College, Cambridge and joined the Royal Navy in 1666. Promoted to lieutenant in 1671, he was appointed to the fourth-rate HMS "Advice" and then transferred to the third-rate HMS "Rupert" and saw action, when a combined British and French fleet was surprised and attacked by the Dutch, led by Admiral Michiel de Ruyter, at the Battle of Solebay off the Suffolk coast in May 1672, during the Third Anglo-Dutch War.