Firstly, I don't think she will be able to get it done at a public hospital anyway, since the EHIC only covers emergency treatment. Even if she can, she would almost certainly need an appointment, and (in my experience) have to join huge crowds in a chaotic and probably rather unpleasant waiting room and wait for a long time for the test, and then for the result.
Secondly, does she know what her level should be, and what dosage to take accordingly? Without her history, I wonder how a clinic here would be able to advise her anyway. Justin, what happens with your mother?
Finally, just in case you come up against blank stares when asking about Warfarin here, the equivalent is called Sintrom.
I agree with Justin though, find a local private clinic and make some enquiries.