There's no difference between landing a helo or a plank on "private land". (This would be a "private" aircraft, I suppose?). You just need land-owner's permission in UK, and adhere to the rules of the air.
The difficulty arises when you try to land a "private" aircraft on public land, ie government owned or military property. Bureaucracy really gets in the way then, even if it is an airfield. Try getting permission to land in a municipal park and see what I mean! Landing public aircraft on public land is much easier, but then that is where military aircraft normally operate from.
Every civil airfield is as much "private" land as your neighbour's paddock, isn't it? You need permission from the land-owner - or his proxy, perhaps in this case Heathrow Tower, to land there...No difference.
And from what I've seen in several years of landing in fields it is invariably the owners of the nags that get dangerously over-excited about helos landing nearby, rather than the far more placid horses themselves.