I have just added this to the map of places to fly your drone at Drone Scene:
Land owner permission not required.
No council bylaws present restricting the use of drones or model aircrafts. This park is does not fall under the National Trust either.
From the planning document: Runnymede Pleasure Grounds (RPG) is a public open space on the banks of the River Thames, mid-way between Egham and Old Windsor. It is held by the Council as Trustee and the Trustee function is delegated to the Community Services Committee.
As mentioned in the warning, this park can get busy, especially on weekends. Would err on the side of caution flying here.
The originator declared that this location was not inside a Flight Restriction Zone at the time of being flown on 02/02/2020. It remains the responsibility of any pilot to check for any changes before flying at the same location.