I wasn't upgraded at the Savoy, but I didn't check to see if there was any availability. I requested one on booking if available. I was confirmed/booked in the Luxury King room, and they were able to give me a 'partial' river view, but it was still in the same room category that I was originally confirmed in. It was a very partial view; only able to see the London Eye and Parliament if I looked just the right way.
Perhaps since I had already used a room upgrade cert to go from the Deluxe King to the Luxury King, they weren't going to upgrade me any further?