I have a suggestion - go to Le Meridien Piccadilly. Although it's not in the Knightsbridge area and it's right on Piccadilly in Mayfair, a few minutes walk from the Fortnum & Mason, towards Piccadilly Circus. It has by far the most amenities compared to all the hotels in London I've stayed - and I have seen several websites refer it as a five-star-plus hotel. One downside is that parking's very difficult in the area.