Not particularly exclusive, bought by NatWest in 2000 and then taken over by Ernst & Cie. So its little more than a brand-name these days, you can effectively buy your way in.
If you want truly exclusive, you have to cross the road and walk a bit further down the Strand to Fleet Street.
Regarding Private Banks and the online world, yes they tend to be a bit further behind the bleeding edge. But then if one can call up one's relationship manager who recognises one by voice without the need for tiresome security questions, then one might understand why expenditure on one's bank's online services is a secondary priority.