I went back to RAF Lakenheath in 1994 to take my daughter to where she was born, and they did indeed have a Burger King. I don’t remember a Popeye’s though. In the mid-70s, there was nothing like that.
The only AFB I’m familiar with currently has a BK but no Popeyes. And the BK doesn’t participate with app deals so I don’t go there much. They also have a little Filipino fast food kind of place indoors in the BX which is pretty good.