As a noun phrase, only 'half a mile' is possible for me (BrE). The other is possible only as a sequence of words, not a constituent, in e.g. 'a [half mile] walk'. Presumably this is the same as the better-known BrE/AmE difference 'half an hour' (BrE), 'a half hour' (AmE), but of course I can't speak for AmE. More @Wikipedia
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