Travellers to Japan need to arrange comprehensive travel insurance before visiting the country, because there is no reciprocal healthcare agreement in place between the UK and the country and treatment in the country can be very expensive.
Hospital standards throughout the country are excellent, and most doctors will speak reasonable English.
There are no specific health problems that you may encounter in Japan, other than food poisoning or sun burn in the summer. Tap water is safe to drink, although the taste can be odd, and many people prefer to stick to bottled water.