We are just back from a weekend in London and we wanted to stay somewhere special too. It wasn't central, it didn't have tube stations very close but buses ran every couple of minutes, and I just loved it. Very very warm and friendly welcome (Vladdy the concierge is great), the staff make you feel like a million dollars and the building is georgeous. It is called The Gore Hotel in Kensington and is just round the corner from the Royal Albert Hall.
It is a real 'boutique' hotel so there is no way it could be called modern! When we arrived we were shown to our room but it was right at the top of the hotel and was very small. We asked about a better room and were given a better one (no extra charge).
I don't know what you deem to be astronomically expensive (The Gore aint cheap) but we were really glad that we made the stretch and booked it for 3 nights.
Have a look and see what you think . . .
www.gorehotel.com