They don't have any power to control airspace above, just like any other landowner.
However they can probably make it a condition of access that you may not take off from their land.
I doubt that could be upheld legally though.
To be fair it's reasonable to try to pre-empt frequent UAV flights around more sensitive spots even if the location is just a beach rather than a stately home.
However I don't have much sympathy due to their recent increasing belligerence towards photography in general.
There has been a recent case where NT tried to charge photographers with photos on Flickr of Whitby - because *their* Abbey was in the view.
It's actually quite difficult to take a view of Whitby without the Abbey in the background somewhere - since it's on a big cliff!