What sort of medical equipment are we talking about here ... nebulizer compressors?
Doesn't anyone ever "look" at medical equipment used in people's homes?
If the cottage doesn't have an earth, then the electrical safety tester won't (shouldn't) work!
Maybe the real issue (not to mention "opportunity") here is (lack of) equipment PM in domestic situations.
BTW, in situations like this I would have thought that the home-bound patient is more at risk from his (unearthed) electric oven, washing machine, instant shower
et al.

PS - another thing to look for are (incorrect) BS-1362 fuses in BS-1363 mains plugs (potential fire hazard). Not to mention use of "adaptors", overloaded (and-or broken) socket outlets, "extension" cables and what-have-you.
Lastly, use of cigarettes at the same time as oxygen cylinders is to be discouraged!