There's no legal way you can do this. The CRB can only carry out checks, through recognised agencies, on behalf of employers (etc) when the person is, for example, applying to work with children or vulnerable adults. Even under those circumstances, the person involved has to sign to agree to their criminal record being divulged to the potential employer.
Even police officers can't check someone's criminal record without good reason. (All searches are recorded and audits are carried out to check that no search was carried out for improper purposes). There was a case in the press where a police officer used the police national computer to check whether his daughter's boyfriend had a criminal record. He was dismissed from the police force and, as a result of the criminal action he then faced, sent to prison.
Chris