(Disclaimer: I haven't actually looked at the law in about a couple of years. My memory may not be entirely correct. You can look this up for yourself, the act in question is the Rehabilitation of Offenders Act 1974.)
One may declare a spent conviction on an application; an employer may ask about any spent convictions but the employee is under no obligation to give the truthful answer (i.e., one can always answer, "I have no spent convictions"), and any knowledge of spent convictions cannot (in general) be held against the person seeking a job.
Note that there are a number of professions where one is always obliged to declare prior offences, regardless of whether spent or not, including your example of a child sex offender applying for a job at a day care centre. I believe that in such cases they are legally obliged to refuse the job application.
The restrictions are far harsher as to when spent convictions are admittable before any judicial authority (which in this case has a very broad definition), where they legally cannot ask, and if asked one is exempt for perjury for failing to truthfully admit. The exemptions here are primarily pertaining to adoption and firearms.
Records of convictions are always on the public record; however, they do not (ordinarily) appear in their criminal record. (A police caution is not a conviction but is on the complete criminal record; a caution is spent immediately upon being given.)