Here is a link to the Cadbury Research Library's LGBTQ Resource Guide . This tells you about the various collections in the library including for example the Noël Coward archive and the Centre for Contemporary Cultural Studies (University of Birmingham) archives.
Coward image courtesy of Cadbury Research Library
Noël Coward: an Entertainer Abroad Online exhibition of photographs and documents from the Cadbury Research Library
Women from The Cadbury Research Library exhibition of photographs and documents from the Cadbury Research Library