If I'm correct, the Subject Access Request deadlines started from the day they first received your request. This further request is most likely delaying tactics.
The Data Protection Act request is a request for information on AN INDIVIDUAL and the bank are therefore required to be able to locate that individual even if you don't have account numbers.
It is important for him to identify himself so I agree with bigmac regarding the extra information though I would put in the letter somewhere the bit about an individual and that you have provided them with enough information to do this so you expect no further requests from them.
Good luck
