I'm not Irish (in this life, anyway; maybe next time around), but I can totally see eating 300 pounds of potatoes a year. Basically, that's a pound a day 6 days a week.
If a pound a day seems like a lot, go get one of those big baking potatoes at the supermarket and weigh it. It'll be about a pound, give or take a bit. So anyone who has a baked potato 6 out of every 7 days a week would do it right there.
Of course, it could be mashed, scalloped, boiled, fried, or potato salad. It could be potatoes and onions or hashed browns for breakfast. Potato chips, too. Roasted, in stews, in soups...
How many do I eat? Not as many as I used to, I've noticed. Maybe only a couple times a week nowadays. In the past week I've had one large baked potato, one serving of potato salad and most of a bag of potato chips. There are weeks on end when I have none at all. But I bet I ate 300 pounds a year of them in my younger years (and, yeah, it shows).