I don't even know anyone personally who has expressed any favorable view of Trump. Yet clearly they exist in fairly large numbers, so I don't think that should prevent me from acknowledging them.
Second-hand anecdotes of people claiming they'll vote for Trump just to see the system come down is not data.
Without data, it may be such a minority of people that it's not worth significant consideration in a discussion. I'm apt to believe it's an extreme minority given it's an extreme view.
In any case you're probably right. Most people who voted to exit the EU probably weren't uninformed. Google data only represents correlation. General buzz about brexit is a more likely explanation for the search trends. Occam's razor dominates.