The Local Government Board (LGB) was a British Government supervisory body overseeing local administration in England and Wales from 1871 to 1919.
The LGB was created by the Local Government Board Act 1871 (C. 70) and took over the public health and local government responsibilities of the Home Secretary and the Privy Council and all the functions of the Poor Law Board, which was abolished.
More information on the Wikipedia page [1].
Details of the records, held at The National Archives here.