About the University of London
The University of London is a loose federation of academic institutions, not a single university with a single set of rules and procedures. You may therefore find that one set of procedures and access arrangements used in one library may not be used elsewhere.
The University of London consists of several colleges (Kings, Imperial, UCL, Queen Mary, etc) which in effect act as independent universities, several specialised research institutions which offer postgraduate qualifications which are grouped into the School of Advanced Study, and there are several other institutions and schools, such as The Royal Academy of Music, and the Courtauld Institute which are loosely affliliated to the University of London.
A complete list of the institutions federated into the University of London is given on its website.
The central building of the university is Senate House in Bloomsbury, near The British Museum. Most of Senate House is taken up by Senate House Library, which along with the libraries of the School of Advanced Study make up the University of London Research Library Services.
The federated nature of the university and its libraries can seem very arcane and intimidating, particularly if you are not a student or academic affiliated to the university. However the best way to approach the University of London libraries is simply treat them as a group of individual academic libraries each with their own way of doing things, that happen to come under the banner of the University of London.