Ha, one of the most famous airports in the world and it does nothing for spotters!
How does the Aviation Experience at BHX do? Is it costing more than it makes? I visited it recently when passing through BHX and found it surprisingly large! Crap views of T1, limited views of T2 but good view of the south half of the runway, albeit it quite distance away. The place was fairly crowded even though the crap wx. £1 entry or 50p for kids, free for passengers, it's not superb for photography but at least it gives us a place to gather. I'm told you don't even get moved on from the main longstay carpark, where you are only 60m or so from the runway and right under the approach.
I can understand the security situation, closing down the visitors centre at LHR might save a few £££ but how much extra hassle will it cause for the local police? Do you think everyone will stop visiting LHR? Phtt, fat chance!