Perhaps, it is best to transfer FB Miles over to Accor Points (is 1000 FB Miles -> 4000 Accor Points deemed good?) and redeem them for London hotel stays.
1000 FB Miles -> 4000 Accor Points would be magnificent value. Unfortunately, it is the other way around: 4000 FB Miles -> 1000 Accor Points. This is very poor value (somewhere in the proportion of 75% devaluation) but that is par for the course when you use airline points on hotel nights with most programmes.
You are never going to get tremendous value from using airline points for hotel nights. If you translate to currency conversion, it would be similar of getting 1 US dollar for 3 GBP so, very poor value. However, very poor value is still better than no value at all so, if you really can't use your FB points on flights or flight-related spend with AFKL, then you might as well use them for something. I am not sure that you will get a lot of expertise here on alternative use of FB points as most of us will use them on flights or flight-related spend as it is by far the best value so you might need to do your own homework on this.