Jeju is not very English friendly as Seoul is, and the older locals would hardly know any English. Make sure you have your map, with directions to places you want to do/go if you are not joining a day tour.
Of course, there might be locals who are proficient enough in English, it depends on who you meet and the area you are in. The menus might come with illustrations... But otherwise it shouldn't be that hard if you use body language, and simple English. You could use Google translate or the like to get though more complex conversations? But generally it should be fine.