I was under the impression that London Croydon had mostly been developed over. I thought the only remaining part of the runway was 120m of concrete? Perhaps I am wrong...
A flyby was held back in 2009 - but I thought that it was literally just a flyby? (Ie not touching down).
As an alternative - there is a rather long (and only slight gradient) on the playing fields to the east, I think they're called Purley Playing Fields. Which seem clear and most certainly able to land a plane there, and it is only on the other side of the road. Getting permission to do that may be tricky...!
However irrespective of that - you will be in the London zone, within controlled airspace, and abiding by the glide clear rule / 1000ft rule you may need to work something out with ATC as well...
You could always take off from Biggin, and request special clearance to do a flyby at Croydon! Perhaps the closest it can get?