Until 1889, the current area of Wandsworth was part of the county of Surrey. In 1855 the Wandsworth District of the Metropolis was formed comprising the parishes of Battersea (excluding Penge), Clapham, Putney, Streatham, Tooting Graveney and Wandsworth. Battersea was removed from the district in 1888. In 1900 the remaining district became the Metropolitan Borough of Wandsworth and Battersea became the Metropolitan Borough of Battersea.
The London Borough of Wandsworth was formed in 1965 from the former area of the Metropolitan Borough of Battersea and the Metropolitan Borough of Wandsworth, but excluding Clapham and most of Streatham which were transferred to the London Borough of Lambeth.From Wikipedia - click for full entry