From the Wikipedia page 
Greenwich was a local government district within the metropolitan area of London from 1855 to 1900. It was formed by the Metropolis Management Act 1855 and was governed by the Greenwich District Board of Works, which consisted of elected vestrymen.
Until 1889 the district was partly in the counties of Kent and Surrey, but included in the area of the Metropolitan Board of Works. In 1889 the area of the MBW was constituted the County of London, and the district board became a local authority under the London County Council.
Now part of the Royal Borough of Greenwich
A history of the District Board of Works building here .