The history of this house and farm is closely linked to that of Itford Farm. For Christopher Whittick's account of the early ownership of Itford (possibly including Asham) see the page for Itford Farm

Sir William Gratewicke of Tortington willed Itford to his son Edward in 1613 and he, in turn, left it to his daughters Frances and Mary in 1625/6. They both died young and Itford passed to their mother, Frances, who took Lyming Dickenson as her second husband. Frances transferred Itford to John Coell and Richard Pagett the younger in 1656.

Asham Farm was still owned by a man named Padget in 1780 and occupied by Aaron Winton. The same owners and occupiers were recorded on the Beddingham land tax assessment for that year for Itford Farm, and the ownership and tenancy of the two farms appears to have been combined into the twentieth century.

By 1790 the ownership had passed to William Russell and the occupier in 1792 was Joseph Martin. A map of Itford and Asham Farms for William Russell in 1790 by Thomas Budgen shows that Asham Farm comprised 184 acres 1 rood and 34 perches of arable and marsh land, and 150 acres 2 roods and 2 perches of sheep down, making a total of 334 acres 2 roods and 36 perches (ref ESROEast Sussex Records Office/AMS 4665). The farms then passed to the Hoper family. From 1818-1831 John Hoper, solicitor of Lewes, owned both Asham and Itford Farms which were both occupied by John Body, and the hoper family owned Asham until 1924.

Frances, Viscount Wolseley had considered renting the house before opening her College for Lady Gardeners at Ragged Lands, Glynde in 1905. Virginia and Leonard Woolf leased Asham House just before they married in 1912, but used the house as a holiday and weekend home. In 1919 the Woolfs moved to Monk's House, Rodmell.

Asham House was occupied by Frank Gunn, farm bailiff to J D Hoper, in 1924 and the same year the Hoper family's connection ended when Kate Anna Hoper sold the farm to Frank Gunn of Asham House, Beddingham, farmer, on 29 September for £4000. The sales particulars included a plan of both Itford and Asham Farms and a schedule of the fields. The property was described as "all that messuageHouse or dwelling,
inc. outbuildings &
orchard, courtyard
or gardens known as Ashham House with the cottages, barns and other buildings and the several pieces of or parcels of arable, meadow, pasture and downland thereto belonging situate and forming parts of Itford and Asheham Farms in the parish of Beddingham aforesaid and containing in the whole by estimation 369 acres 1 rood and 14 perches". In 1932 Asham was sold to the Alpha Cement Company who had opened the nearby cement works. The proximity to the works eventually made the house uninhabitable. The cement works closed in the 1970s and became a landfill site which expanded towards Asham House. Eventually the owners of the landfill site applied to expand their workings to include Asham House. After a failed campaign by various Bloomsbury Group devotees to save it, and a number of photographs had been taken and floor plans made, Asham House was demolished 12 July 1994.