I agree totally with Who Has Control -
Last Saturday I flew Netherthorpe to Norwich via a turning point directly overhead Fenland Airfield. Although I was at 3000' QNH, strictly speaking above their ATZ, I still contacted Fenland Radio to advise them I was approaching, gave them my altitude/heading and intentions etc, just to warn them of my presence.
Fenland Radio thanked me for the call - I'm sure that regardless of whether or not it is strictly necessary, it is good airmanship - not to mention courteous - to let them know I'm passing.
In doing so it also helped me out a little because another aircraft was also transitting above their ATZ north-south, and Fenland were able to warn me to keep a look out for the other guy.