Credit Rating
Actually I had a conversation about this with my bank yesterday. The feeling was that I would need 6 months of UK payslips before anyone would make me an offer. However, as I had been with my Bank for some time there was a possibility that they could put me in touch with another lender who would be prepared to help.
So my simple advice would be to ensure that you retain your UK Bank Account and if possible pay regular (if small) amounts into it on a monthly basis.
Most financial institutions want your business but need reasons to believe that you are a good credit risk.