As Ethel states, the closest thing you can get to a CRB check is a copy of your 'police record'. That should show everything that the police have on file about you.
Unless there's been a recent change to the rules, which I'm unaware of, Ethel seems to have made a very rare error. The police are allowed 40 days (not 28) to respond to your request.
A potential employer's request for an enhanced CRB check (which can't be carried out unless you sign to give your permission) may trigger 'job specific' enquiries. (An enhanced CRB check can show any information which a senior police officer, or other relevant agencies deems to be relevant). So an application for a teaching post might involve information being sought the General Teaching Council or from the local education authorities who've previously employed the job applicant. An application for work in a children's home might mean that various 'social services' bodies will be contacted. It would be impractical to let you seek a 'general' (rather than 'job specific') enhanced CRB check as it would waste a great deal of time of those various external agencies.
Chris