The United Kingdom probably has one of the most varied in bathing establishments so it is going to be a really interesting place to start exploring. Perhaps it reflects the migration patterns of various immigrant populations over the years. There are the old Victorian Baths, some of which still exist which were originally constructed when men returning from the Crimean War yearned for the Turkish style bath. There are a few hamman/ turkish baths and there are saunas all over the place. Spas are also very popular with added therapies.
The etiquette will vary I assume as the UK is not one for supporting nudity, and expects swimwear to be worn in saunas. Part of the experiment and the journey will be to discover what is allowable and practised. Now where do I start. Please send any suggestions of places to review.