You can go and stay in the house!
I knew it was filmed at Simon Groom from Blue Peter's dad's farm but I didn't realise their farm was the actual house where Anthony Babington had lived - I always assumed they'd just picked a house that looked about right.
And (like most farms these days....) Simon Groom and his wife now do B&B.
I know where I'm going next time I get a weekend off....