DWP How long to access records from storage?

In an ongoing battle for SDP back-dating with ESA. After 4 months of weekly phonecalls and a lot of enquiry line staff telling me lies in order to get me off the phone I was told by a manager I had to send over historic tennancy agreements. I did so recorded delivery and a week later went though another escalation and the lady I spoke to put me on hold, said she had spoken to Belfast and they have received my letters and are processing my claim for SDP now and will be done by this afternoon. "The funds will appear in your bank before the letter arrives telling you how much there's no need to call us back again.".... 5 days later nothing in the bank so I called up and the last note on the system supposedly says they need to access my records in storage?? Why tell me I'm getting paid this week unless they know for certain? Is there some file on me in a storage facility somewhere? And how long should I roughly expect to wait for them to be posted through to benefits centre Belfast?