The "Brandon Lee" case came to light in 1994. It was not until 2002, the date of the Soham murders, that the educational establishment went into panic mode with background checks. Before that date, agencies, for example, would tell all candidates that checks would be done. Often they were not. There was a lot of catching-up!
Tighter safeguarding would not necessarily have helped the victims of the Soham case, since Huntley was trusted as the boyfriend of their teaching assistant. The current application form for a DBS contains a question on cohabitants but - given the longevity of many relationships - it looks like a token gesture to police something unpoliceable.