I wouldn't worry too much if I were you hyakuretsuken as even paying full price for medical care in Japan or seeing a doctor is quite inexpensive compared to the states ( I don't know about the UK). Please see my post "
Emergency Medical Care in Japan" when I had to visit a doctor on an emergency while on a tourist visa a few years back. Trust me, I believe you will still be able to afford it on your salary while on a tourist visa.
Also, see this video on You Tube,
Its Shocking How Cheap Health Care is in Japan from a woman actually living there. I think you'll be surprised and a little relieved.
Full cost doctors fees will not break you I'm sure and some doctors, especially one you go to on a regular basis and understands your situation, may just give you a break. I can't promise that, but it happened to me (when I didn't have NI while living there back in the day) and a few others I have read about recently on the net.. Either way, full priced doctor visits and prescriptions are very, very reasonable in Japan and you should be able to afford it. Good luck and don't worry about it. Maybe some others will have more information to add on this subject to alleviate your fear.
Also, in Japan, when you apply for NI, all pre-existing conditions ARE covered by law and you will not pay any more than anyone else. Japan's NI health care system ranks second in the world behind France.