For my generation of (elderly) speakers of British English, 'I haven't a clue' is the only correct form. However, with HAVE as a full verb, 'I haven't ... ' is now uncommon.
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fivejedjonInterestingly 'I haven't a clue' is still commonly heard; it is almost a fixed expression.It's also common in the US, though I hear the other "I haven't go a clue." as well.