Hi Natalie-Layton: Welcome to the forum. I would think a trip to the Birmingham Main Library would give you some leads on the main dance halls in Birmingham for the years you are researching. There are some references on this forum of members memories from such dance halls as Grand Casino Ballroom which was on Corporation Street, Amies Dance Academy on Chain Walk in Aston. I know of the Albert Hall in Witton Road, Aston, The Palais de Danse...not sure where that was. The Tower Ballroom, Edgbaston, Tony's Ballroom,Hurst Street owned by the Kirsch family, the West End Ballroom,
the Ritz Ballroom, Birmingham.
Members of this forum may know of others. Good luck with your research.