Green’s Dictionary of Slang

to wash; thus as n., a wash.

1909		J. Ware Passing Eng. of the Victorian Era 165/1: Lambeth (Peoples’, S. L.). Wash. From the popular cleansing place in S. London being the Lambeth baths.
1953		J. Franklyn Cockney 178: The extent to which the Cockneys welcomed such aids is indicated by the slang term to have a Lambeth, meaning ‘a bath’; from the big and well-patronized public baths maintained in that borough.