Well, I don't think Brazil would be able to "sign up" to either JAA or FAA, unless they make themselves a state of either the European Union, or the United States of America.
Arguably they could use the guidelines of JAR-FCL, enact them into local law and be considered the equivalent of a JAA country/registration/license. However, when EASA takes over flight crew licensing from JAA, they've got to become member of the European Union before they can adopt the same rules.
So I guess you either have to train in Brazil, do the Brazilian exams, get a Brazilian PPL and then try to convince the CAA to render it valid to fly a G-reg, or something like that, or do it the other way 'round. That is, if you want to be able to fly planes both in Brazil and the UK.
Unless, of course, you manage to find a Brazil-registered plane in the UK, or the other way around. That way you can fly in both places on just one PPL.