I bank with Coutts, Classic old fashioned service. However you are not there type of business. The best option is one of these internet banks for free banking and simplicity. Cahoot or egg or that 1st direct lot all seem to work well.
I also use Carter Allen which are a subsidiary of Abbey or Bank Santander as they are now. Not a bad account for the low end of Private Banking with a good Jersey office.
Barclays are a pretty shocking, they make money despite themselves. It will be interesting to see how things pan out if the merger with ABN Amro goes ahead.
I think that times have moved on and the classic banking experience you are looking for is a thing of the past.