Have you considered finding a financial institution willing to provide a white-labeled banking service?
My understanding is a white-label arrangement will provide you the deposit accounts (with account numbers & sort codes) as well as means of transfer (cards, direct debit, etc). This will save you having to apply for license to accept deposits while offering something that looks and works like a real deposit account.
The main upside is that you'll essentially be riding on somebody else's banking license and letting them worry about the hard stuff... Leaving you to concentrate on making a good online banking product
The biggest downside of course is your partner. It could hinder your objective of providing a more transparent service
IIRC https://simple.com went down this route.