What i'd really like to see is a London centric bank (or perhaps building society), one that understands the rental market and the ownership market. It's insane that people (myself) pay more to rent somewhere than to buy somewhere, yet are hamstrung by the fact that either they don't earn enough to afford to buy, or don't have a deposit to afford to buy.
I thought Metro Bank might be that, but i think they're more focussed on expanding outside of London.