Some changes of name are registered, or “enrolled”, with the Supreme Court of Judicature. Five years after a Deed Poll has been enrolled, it is transferred to The National Archives in Kew, Richmond, Surrey. The National Archives are open to the public, and you can therefore search through the Archives for previous name changes.
However, enrolment is fairly costly, in particular because a solicitor needs to be involved in drafting a Deed Poll that is to be enrolled. Also, enrolment involves publication in the London Gazette of the change of name; as many people who change their name, do so precisely because they do not want to be found, this is a factor that causes many people to decide against enrolment. As a result of the extra costs and publication, many people do not enrol their Deed Polls and searching the Archives will have only limited success.