I have a first direct account which is very good, but thats Internet and Phone. I also have a smile and egg account again both of which are good. Finally I have a Barclays online account which is also very good. The question is why would you want one, i.e. what purpose would it serve ? Thats a genuine question, I'm not suggesting you shouldnt. I think the best option is to have an Online account with a high street bank that way you can access it easily and deal with stuff on line but if you need over the counter services then you can use them.