Though there are a slew of new banks coming on-line, Tide is aiming for the business market with no fees (they make their money on various services that a banking customer might use and they're not unreasonable).
The first thing to say is it very easy to sign-up. Just present a valid ID to the app and take a photo of it, then clever magic works out who you are (which you confirm) and then it asks what company you're going to use (it looks up your details in Companies House).
You then get an account (a real account number and sort code).
Once set-up you can do all sorts of things through the app, like invoice customers, pay invoices from suppliers etc. When invoicing it can track incoming payments and send out reminders if the customer doesn't pay. If you need to take a credit card payment, it can do that too, just scan the customer card, it will then ask the customers for the CCV (the number on the back of the card) and that's it (there's a fee for handling the payment, that's where Tide take a small percentage), but no card readers to worry about etc.
The service is currently in alpha to a few select customers (the alpha client looks very nice, though the version tested was a sandbox'ed version so not doing live transactions, the real alpha client does the same thing in a live environment) and it will hopefully launch in beta very soon.
Though it's mobile first, all services are also available on-line (web access) and there's a (developing) API on to everything, so if you want to build your own client and offer new services, you'll be able to do so.
If you want to sign-up for access, use this link Tide Preview.