To the best of my knowledge there never were UK sweats/saunas/hot rooms of any sort.
See above links. Stone bathouses built in the Gaelic-speaking areas of Ireland and Scotland. Some fragments of ceremonies remain, but the structures and ceremonies are not like Indigenous American sweat lodges.
As for smelly Europeans, well, it depends which culture we're discussing. There was never one, uniform, "European culture" any more than there was (or is) one, uniform, "Native American culture". In antiquity, there were many different tribal groupings across mainland Europe and the six Celtic nations. Hygiene standards varied, along with other aspects of culture and religion. The ancient Irish warriors were required to bathe daily, even if they had to break the ice off a stream to do so. They were also required to unbraid and rebraid their hair every day. There are tales of the Irish finding people from the mainland smelly.
That said, with the advent of Christianity and its taboos around nudity, mainland Europe got pretty smelly for a while there. In some areas daily bathing is still not practiced, and it seems the first waves of invaders in America were a reallly smelly, filthy crew. I'm sure the Indigenous folks didn't want to go anywhere near them. Just like the Irish and Highland Scots had avoided these smelly people from the mainland when they invaded there.
The only other type of hot room that I have ever heard of is the Swedish sauna, which is steam.
There are dry heat saunas and steam saunas across Scandinavia and Eastern Europe. In some of the more remote areas of Eastern Europe, where Christianity never gained solid footing, there are some songs and prayers used in the saunas, and different sauna rituals for different cultural purposes. I know this from a family member whose father grew up with these customs.
To me this really is a new form of greed. Knowing that if he sells Sweats then not only will people, such as ourselves, criticise him and condem him he's hoping to get round that by creating a history of European Sweat Lodges.
The irony is, there are legitimate traditions, from individual "European" cultures, that are not based on stealing from NDNs. What this guy is doing is not legitimate in any of the above-mentioned cultures. It's like the nons in America who are doing the same thing - fake Inipi with some misunderstood and misapplied terms from other languages, hoping to camouflage their theft and throw the NDNs off their trail. It offends all our ancestors. And if any spirits come, they will be confused, and most likely offended as well, because these people don't know how to interact with them respectfully, or even how to tell if a spirit is helpful or harmful. These people do all sorts of harm.
ETA: I'm looking over his site. No. Just no. "Smudging" and "Water Pouring" are not European. Nor are all the fake-NDN accoutrements in his photos. His testimonials are from the newage, "firewalking" crowd, who don't bother with his camouflage and just say, "sweatlodge". He speaks of "Celtic Shamanism". Like with NDN traditions, "shaman" is an outsider, anthropologist term, and not relevant to actual Celtic practices. When they can't get away with saying "Indian", they try to say "Celtic". No, still a lie. This just has fraud all over it.
This quote really gives it away, as well:
http://www.spiritlodgeacademy.eu/academy/deepening the connection to your own roots, our Creator and the whole of creation,
Since there was no one "European" religion, I'll go from the Celtic and European religions I know of. The pre-Christian religions in those areas were polytheistic. Multiple deities, multiple creators. So unless he's now doing Christian Sweat Lodge, he's ripping off even his theology from what little he knows of contemporary NDN cultures.
And here:
http://crafts.maartenelout.com/ He'll sell you a rattle with Kokopelli on it... Who we all know is a traditional symbol of European spirituality. < / sarcasm >