I have just added this to the map of places to fly your drone at Drone Scene:
Land owner permission requirements unknown.
The Needles and some surrounding areas are National Trust land but there are gaps. I parked and TOAL'd from the Disabled car park during off season near to dusk which meant the attraction was closed and footfall was low and I wasn't challenged by anyone.
Wouldn't recommend attempting "in season" as it is a very popular attraction and the car parks, the attraction and the beach is very busy during peak times.
The originator declared that this location was not inside a Flight Restriction Zone at the time of being flown on 14/02/2023. It remains the responsibility of any pilot to check for any changes before flying at the same location.