First Direct is great; I've been an account holder for a bit over ten years, after getting an offset mortgage with them. I've once needed physical contact, for which they have an arrangement to use your local HSBC branch. Otherwise it's just as you say: ring up at 2am, answer within 5 rings, incredibly helpful staff.
Frankly, I'm astonished it's survived. It was always an 'internal startup' in a big bank (Midland, before they were taken over) and I would have thought the bean counters would have successfully lowered service standards by now - or at least stuck a heavy fee on and marketed it as 'premium'. But no, it just keeps rolling on, delivering excellent customer service, decade after decade.
I don't even like HSBC, but it's so good I don't want to leave.