Want to move to another country for career purposes after school, what do I do?

I’m currently a year 10 Australian high school student, about to go into year 11 and I currently want to be a game programmer, and for career reasons I’ve realized that I’d probably want to move to another country, currently thinking Britain/Europe as Australia doesn’t have that many huge game development companies, if any, and I’m not that big of a fan of moving to America. So I was wondering, do I study Uni here and get a degree then move to Britain, or move to Britain and study Uni there?
I’m enrolled in an ICT VET so I should be able to get a low level job with that certificate after graduating high school in order to be able to save up enough money to move there and get a house/apartment/rent, and pay for uni, etc

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