I have flown here on several occasions. I checked extensively for any specific restrictions and could not find any. I think I may have found a reference to drones on an old Facebook post from the park’s FB account but I could not find any details of current exclusions.
I also checked the notice boards around the park and there was no mention of drones (but a lot of focus on the banning of fishing and BBQs).
Obviously, care should be taken here as it is an SSSI so you need to ensure you do not disturb the local fauna.
Some of the colours and textures you can find in the park look great from above (e.g. like this).
Where did you see the ‘no drones’ statement, @speedracer66?