1. Sketch
2. Nopi
4. Aqua Shard
6. Gilgamesh
10. China Tang
11. Barrio East
13. City Social
14. The Fable
Nice big mirrors, lovely hand soap and taps that create a little river to pool water over your hands. Delightful.
Nearest station: Farringdon
15. Claridges
And if you're stuck, here's a map of all the free public toilets in London