Actually, in a idle moment last week I checked the Savoy for the first weekend in June, when we are visiting (since it's very close to the main reason for our visit) and a room could be had for a 'mere' £250pn !! So give it a shot.

I bet there are cheaper rooms at the Sofitel St. James than the one we had. I'd investigate.. I reiterate only because the hotel's location is so great.

Near Sloane Square:
11 Cadogan Gardens Hotel
www.number-eleven.co.uk

Standard (but charming) double for 250 pounds.