I have just added this to the map of places to fly your drone at Drone Scene:
Land owner permission not required (if using public footpath, see below) .
This is an English Heritage site so you can’t take off or land within the site itself without their permission.
I parked in the EH car park (£3 for non-members) and walked to https://w3w.co/cardinal.hotels.satellite, which is on a public footpath. There was a handy tree stump to set up gear clear of the muddy path.
Accessibility: the footpath is accessed via kissing gates and a few steps, and can get very muddy in wet weather.
Hazards: the castle sits on a rocky outcrop roughly 120m high, so your drone ceiling may need adjusting to fly higher. However there were several low-flying light aircraft when I visited, and they may not all maintain full clearance above the castle. Also dogs and dog walkers.
The originator declared that this location was not inside a Flight Restriction Zone at the time of being flown on 17/10/2020. It remains the responsibility of any pilot to check for any changes before flying at the same location.