Stayed at County Hall on a 7-night reward stay and, for our purposes, found it great. Only Gold at the time, but upgraded to a lovely room with a great view of Big Ben and Parliament. Concierge Lounge was closed for renovations so they comped us to breakfast in the restaurant for our stay - a great treat. And the breakfast staff "held" our favorite table each morning. As a tourist we were expecting to walk a lot, and the 5 minute hike to the subway station was no problem.
But based on comments above, plan on trying Chancery Court next time.