I use my local credit union to get cash. I visit about once a month and withdraw a wad of cash that pays for my day to day expenses.
I also visit my bank about once a month and do about 4 transactions. This usually involves the payment of utility bills and lodging dividends (the handful of companies that are still paying divvies). I don't usually use the DD system probably because at the back of my mind I am always thinking of changing provider but in the end I never do.
I could pay my utility bills in the post office but I am not sure what I could do with sterling dividends. I could take a script issue but I don't want to do this.
Some bills such as annual UPC and house and car insurance could be paid with my credit card.
Paying for things like new drivers licence, passport, renting an apartment abroad type of thing need for me to issue a cheque or make a money transfer. Then again I suppose I could purchase a draft or postal order (do the still exist) to make occasional once off payments.
I reckon I could survive without a bank account. How people might pay me would be an issue though.