I must be odd. I'd hate to pay increased premiums for years afterwards (upto 5yrs isn't it?) and the thought of someone potentially riding around on my property for free (who cares if I'd be paid out) would really really rankle me.
Plus the fact that a couple of months down the line (and thereon after) they'd be noising around again to see if the garage or shed had been refilled.
I'm not into keeping the criminal economy topped up. Insurance (in my opinion) isn't there as a backup/catchall. Its the additional thought of someone having something of mine that'll stop me storing anything outdoors.
Same with a car, if a crim broke into my car I'd be incredibly pissed off and probably not put a claim in (even though the damage would be circa £500).