Perhaps you all missed my informative post further up about not being on the electoral roll not meaning automatic decline for credit. It's all up to the individual lender, but decent lenders would ask for further information to verify your identity if you're not on the electoral roll rather than flat-out decline you.
Most lenders have an appeals process, and if you're declined credit, write to them enclosing documents to verify your identity (certified photocopy of passport and recent utility bill) and your income/ability to make repayments (3 months bank statements or payslips).
They rarely volunteer this information (because it's more paperwork for them if you appeal) but if you supply the correct information and it checks out, your credit could be approved. Regardless, they should write back to you with a decision.
This isn't just a "why not try this" suggestion, this is from someone who worked in underwriting at a credit card company. If a financial institution is a member of the FSA (pretty much all of them) then they must be fair and equitable in their lending policies - refer them to the Banking Code if you feel this is not the case.