I have just added this to the map of places to fly your drone at Drone Scene:
Land owner permission requirements unknown.
On the approach to the Castle entrance on the A595 turn left at Devonshire walk, you can can park in the car park (£1.20 for an hour)
And you are in a park adjacent to the Castle walls. The castle is managed by English Heritage.
The originator declared that this location was not inside a Flight Restriction Zone at the time of being flown on 02/02/2021. It remains the responsibility of any pilot to check for any changes before flying at the same location.