I find this a little remarkable on your Banks behalf espiecially if you already Bank with them personally and have tried to present them with a business plan!
I cant see what their risk in opening you a business account for you is, my business account is just like a normal current account, I dont have an overdraft facility nor did I request a card for the account, it is literally just for paying chqs in and for providing customers with BACS info etc.
Perhaps you should approach another high street branch (im with HSBC) Im sure the would help, I would also move all my personal accounts to a bank that actually values your affairs and wants to help you.
Good luck with your business