I'm UK based as well and also looking into getting a stool test. What you are wanting to test will influence which company you go with. For instance, is it microbiome, fungal, parasites etc? I can tell you that there doesn't seem to be one company that does everything. Many overlap in what they offer. Although many U.S based companies, that doesn't mean you can't use them. Most seem to cater for worldwide patients but not all of those allow a patient to directly request a test and instead require a registered practitioner to order it on behalf of the patient.
A UK based company that has become popular is Biomesight. You can buy their test without needing a practitioner and you can also utilise some online tools like Microbiome Prescription with the results from a Biomesight test. They use 16s sequencing (which I don't fully understand) but it seems that it's solely focused on bacteria testing and therefore doesn't test for things like parasites and fungal infections.
Genova's CDSA/P does include fungal and parasite testing as well as some microbiome bacteria. I'm not sure how it compares in microbiome testing to Biomesight. There is definitely overlap but I think Biomesight covers some things that Genova doesn't. Genova does require a practitioner to order theirs tests but they list registered practitioners on their site and there's some in the UK.
Hopefully someone who knows more about this can chime in with more information.
Lastly, I'd recommend asking any further questions in the Gut section of this forum as you'll be more likely to get people answering who know more about this area.
Ive also done stool microbiome at least 5 times. I did not find it nearly as helpful as the doctors data test which covered so many aspects from parasites to fungal to pancreatic enzymes to inflammatory bowel disease. (One of the problens with the microbiome tests which pick up short genetic sequences of bacteria is that we have so many bacteria in our guts then when you get back your list of the hundreds theyce foubd it depends on which happened to be in the sample. So take two samples even from same stool sample, and the trst results will differ. Youre left with a mess of data. I was taken down several false leads from garbage data. For major bacterial dysbiosis, tha is typically picked up more clearly by non microbiome tests that use old fashioned growth. Doctors data test does that too. Have a look at the sample report and see if theres anythibg missing that you are interested in.