I guess it is quite difficult, because most of the doctors in Japan cannot speak English fluently.
Even if the hospital claim to provide English support, their English skill are limited, not many of them can communicate with you smoothly. Most of the staff cannot speak English especially the receptionist. It would be better to call them and ask whether they can speak English or not.
Japan's National Health Insurance program allow people to visit hospital at a low cost, so they are always crowded.
You may have to wait in line for 2 hours before you can see a doctor for 10 minutes.
If you don't want to wait, you better go there early in the morning before anyone else.
Also, doctors are people too. Better go there in the morning when they are fully energized, rather then after lunch when they are sleepy and tired.
Sometimes you may feel you were treated poorly in the hospital, but consider the fact that doctors in Japan are extremely overworked and underpaid. They need to handle at less a 100 patients a day, speaking another language didn't help either.
There is a Japanese saying "Omoiyari" which mean consideration without verbal communication. Keep that in mind and it will serve you well in your life.
If you're living in the city, you can find a health care facility with English support, however, there is only a few in the countryside.
Please let us know, if you know any health care facility with English support, it will be helpful for other people, thank you.