I couldn't actually tell you the reason for the exclusion zone but my guess is that the UK didn't want a wider conflict, we wanted hostilities localised in the Falklands were we were fighting a war of liberation, not the whole South Atlantic or Argentina as a whole. So while that's technically true, for proactical purposes the exclusion zone existed.
Incidentally did we actually declare war on Argentina, I can't remember it being mentioned when I read something about it. Although it did mention civil servants having to go back to WW2 records to see how a nation actually went about declaring war

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