Both of them are correct.
Some words like this are confusing in English.For example:
American history teacher
It has two meanings:
1- That teacher is from America and he teaches history.
2- That teacher is teaching America's history.
The meaning of these kinds of phrases depend on the sentence.
It doesn't really work to string adjectives together with hyphens like that. You would have to say that he is a well-educated Oxford-educated politician, but the repetition is awkward. I would use a well-educated politician who attended Oxford.