Why does harry not goto gringotts and get everything he has and leave the UK?
Once Harry is out of the UK he can get a new wand and learn wand-less Magic as well as other types of Magic.
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Author's response
Harry really doesn't have a lot of resources. He's mentally damaged, and just wants to have some control in his life. In England, he knows the rules, layout and how people react. In another country he would lose that small thread of control over his life he's finally gotten.
This story has a bit of a build up, but shouldn't take too much longer.