Hi Sarah, sorry that it took me quite a while to reply this time.
I am curious as to whether you are aware of this place and if you have visited.
A little oasis in Alexandra Palace
Alongside their high-end saunas, the thermal spa package a pretty reasonable £26 for three hours also includes hydrotherapy pools, a hammam Turkish baths , plunge pools and more.
Having said that, I do not like the idea of using a steam room when you are unable to clean it before you sit down.