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.