Well, it's just that the Churchill and the Andaz London are both cat 5 hotels. With the possible exception of the Highlands Inn, I would bet ANY other hotel in cat 5 is a better use of points, especially given that you are using it for a weekend.
One room for one night at the Park Hyatt Paris would set you back E550 or more, maybe considerably more, for example! Think big with category 5 hotels.
In fact, if the PH Paris is available, why not take Eurostar to Paris for the weekend and do just that? You'll love it.
Incidentally, if a hotel is not available, you can try calling the hotel directly as on occasion they will open up additional award inventory, particularly as time gets close.