In 1870-72, John Marius Wilson's Imperial Gazetteer of England and Wales described East Harnham like this:
HARNHAM (EAST), a tything and a chapelry in Britford parish, Wilts. The tything lies near the river Avon and the Bishopstoke and Salisbury railway, ½ a mile S of Salisbury; and has a post-office under Salisbury. The chapelry was constituted in 1855. Rated property, £990. Pop., 461. Houses, 79. The property is divided among a few. The living is a vicarage in the diocese of Salisbury. Value, £70. Patron, the Vicar of Britford. The church is good.
GB Historical GIS / University of Portsmouth, History of East Harnham, in Salisbury and Wiltshire | Map and description, A Vision of Britain through Time.
Date accessed: 27th April 2017
Click here for more detailed advice on finding places within A Vision of Britain through Time , and maybe some references to other places called " East Harnham ".