A succinct outline of British railway history is contained in "The Oxford Companion to British Railway History", edited by J Simmons and G Biddle, OUP, 1997, ISBN 0-19-211697-5. It has the advantage of referencing a wide range of sources for deeper study of a subject.
There is also Christopher Awdry's "Encyclopaedia of British Railway Companies", Guild Publishing, 1990, previously published by Patrick Stephens Ltd. (No ISBN) Covers even more companies than those mentioned in the Oxford Companion.