He was succeeded by his second but oldest surviving son, William Meriton Eaton, the second Baron, and a notable collector of mezzotints.
He never married and on his death in 1902 the title passed to his younger brother, Herbert Francis Eaton, the third Baron.
He was a Major-General in the Grenadier Guards and also served as chairman of the London County Council from 1912 to 1913.
He was succeeded by his son Francis Ormond Henry Eaton, the fourth Baron.
He fought in both world wars and was awarded the Distinguished Service Order.