Elliot was born to influential and distinguished family that included several powerful politicians and diplomats. After entering the navy at an early age he served through several of the decisive battles of the French Revolutionary Wars, seeing action at Genoa, Hyères, and Cape St Vincent and under Nelson at the Nile and Copenhagen. He had graduated to his own commands by the outbreak of the Napoleonic Wars, being described by Nelson as one of the best officers in the navy, and served with distinction in the Mediterranean and in the East Indies, where he took part in the Invasion of Java. Left without significant employment after the end of the wars with France, Elliot took up politics, with the support of the Duke of Clarence and his relatives already in government office.