You must be 21 years of age to purchase alcohol in the U.S.A. Disney are quite strict on asking for ID, so don't ever risk it and always carry some ID with you. I'm into my 30's and still get ID'd, and it's getting to the point where it's starting to be a compliment. Some of our more mature fans know what I'm talking about.
What's specific to guests visiting outside of the U.S.A. is:
"All Guests visiting from outside of the United States are required to present both a valid passport as well as another form of government-issued photo ID from their country of origin. Foreign driver’s licenses or ID cards are not acceptable by themselves."
So you have 3 options to get successfully served at Disney World:
1) Show your real passport
2) Show a paper photocopy of your passport with another form of government ID (E.G. your driving license).
3) Show a photo of your passport on your phone with another form of government ID (E.G. your driving license).
We've had readers tell us that their UK driving license is usually enough, it can depend on the cast member. For example, at the Rose & Crown at Epcot, all those bar staff are English and know a valid UK driving license when they see one. However, the Sake servers at Japan likely won't. While your mileage may vary, you should make sure you have 1 of the 3 above to make sure you can get served.