He was educated at Christchurch, Oxford. graduating in 1869. On ordination he became rector of St Nicholas, Guildford, Surrey. In 1871 he moved to London as curate of St Paul's, Knightsbridge. In 1874, when a mission church was built at Graham Street, Pimlico, Eyton was placed in charge. He remained there for 12 years.
In 1883 he was appointed sub-almoner to the queen and in 1885 a prebendary of St Paul's Cathedral.
In 1884 he became rector of Holy Trinity, Upper Chelsea.
Member of the London School Board, elected for Chelsea in 1885 and 1888, standing down in 1891.
In 1895 he was made a canon of Westminster Abbey and rector of St Margaret's, Westminster. In January 1899 he suddenly resigned his clerical posts, with reports saying his health had broken down and he was going overseas to recover.
He died in Bathurst, New South Wales in 1908.