¿Cómo dices esto en Inglés (UK)? I major in International Communications Studies/My major is International Communications Studies

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You would simply say ‘I studied International Communications Studies at e.g Bristol University’ or ‘I got my degree in International Communications Studies from Bristol University’. If you want to be more formal you could say ‘I read International Communications Studies at Bristol University’. If you ‘majored’ in two subjects, it would be referred to as a ‘joint degree’ or a ‘joint honours degree’. If you study a subject that has a ‘with’ in the title e.g. Criminology with a Psychology then this means that the Criminology is the major part of the degree and Psychology the minor part.
However, if you did express it as I ‘majored’ in International Communications Studies everyone would understand anyway.