I have a current account with Metro Bank, with whom I also have savings. Everything is online apart from them initially sending a debit card to me, which I managed to intercept from the mail without my OH seeing. There are no account charges and no requirements to have active direct debits.
I assume they'll send me an annual paper statement for tax purposes, which will show only interest paid (zero) and tax paid (zero) but as I usually deal with the mail and finances and she takes no interest provided I keep her supplied with flowers, shoes and handbags, and as we'll receive something on paper relating to the Metro savings too, I am not overly concerned about that.