Natural England
See our English Heritage and National Trust sections to learn about flying over their properties.
As per the CAA Drone Code - you can fly small drones and model aircraft that are lighter than 250g (and now UK marked drones) at residential, recreational, commercial and industrial sites. However, many people at these locations won't realise that you are also legally allowed to fly over and/or film such sites as demonstrated in these videos.
Natural England often has responsibility for many SSSI sites which are more sensitive than those of the National Trust and English Heritage. The CAA Drone code has a section dedicated to flying over SSSI sites.
Note The Wording
"Flying may be restricted at some Sites of Special Scientific Interest (SSSI) where that flight may disturb animals or wildlife"
Just because the site is an SSSI, this does not automatically mean it is illegal to fly here. You need to look at local byelaws and the site. For example, flying over an SSSI protecting nesting or rare birds would be a no-no, whereas flying over an SSSI fire for protected fauna would - in my opinion - be fine as the drone is not affecting or upsetting the item/area protected under the SSSI legislation.
Plan Your Flight
The key takeaway is that you "Do not fly where you’ll disturb or endanger animals and wildlife". Flying at these sites just because you can when you know it may upset nesting birds or other wildlife will not do the drone hobby overall any good at all. Think, be a considerate pilot.
Natural England doesn't have a blanket ban on drone flying. Some sites are a no-no, at others it's allowed and some you need permission for. This differs slightly to the National Trust and English Heritage as it's directly mentioned in the CAA Drone Code. You need to check for local byelaws or look out for local signs and then follow any restrictions that apply regardless of whether or not you are taking off and landing outside of the Natural England site boundaries.
The following national authorities provide information on SSSIs:
Airspace Misconception
Contrary to popular belief, English Heritage doesn't have the authority to assert ownership over the airspace above their historic properties. The regulations governing airspace ownership in the UK are under the purview of the Civil Aviation Authority (CAA) and adhere to international laws. Consequently, Natural England does not have the ability to regulate or restrict the use of airspace over its properties.
Other Interactions
There are three likely interactions you'll deal with as a drone pilot. Those with the general public, the police and employees (including security) of companies.