Look at the detail of the listing - for both the house and grounds.
"From 1942 the park was used as a military hospital by the American Forces, and subsequently, at the end of the Second World War, as a prisoner of war camp. In 1943 the House and park were bought by the Corporation of Swindon, with a view to establishing a university. "
Allowing charging for access, or carparking should be resisted at all costs. I personally don't see a problem with leasing the land to an operator, whos aims to gain a return by improving the attraction.