If this were not a name, and were used in a sentence (eg, I attended a Britain English institute ), it would not be correct. But names do not have to be grammatically correct!
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AvangiBut names do not have to be grammatically correct!That's true, but I would still expect "British English" instead of "Britain English." So while I would not say it's "grammatically incorrect" I would certain not trust the English that I would be taught there.