For sites that have a “no drones” policy it will still be worth your while approaching them.
First though, it would be a good idea to upgrade to an insured GADC member as well as all the benefits of a full member you will have a 5 million pound public liability insurance. Also look at getting an A2 C of C qualification
Armed with those you can then inform the bodies who are imposing restrictions that you are a qualified pilot with PLI thus meeting their requirements for commercial pilots but A: This is a private project with no intention of commercial gain and B: it is to benefit schoolchildren for whom an aerial photo or video is likely the only chance they will get to see and to appreciate the Roman remains.
If you still find them unco-operative then all is not lost. There may be ordinances or bylaws (often of dubious legality) in place that purpot to forbid you using the authorities land to take off or land. Use a public footpath or a road outside the authoritie’s boundary.
The airspace is regulated by the CAA. They are the sole authority for making airspace free, restricted or prohibited. Drone Scene shows the up-to-date permanent and temporary restrictions. It can be a wee bit daunting on first time use - do not hesitate to ask for advice and guidance in here on any proposed flight!
You can overfly an historic site at a reasonable height. In the summer you can often get better pictures at the beginning or the end of the day when people aren’t around and the long shadows throw ground features into sharp relief.
Practise flying until it becomes almost muscle memory, Then you can concentrate on filming. Look confident and smile a little while you are doing so. Act as though you have a right to be there (hint: you do!). Then the only interaction you will get with the public is them asking questions about the drone. Show them the screen, apologise that you are busy with a school project and let them watch from a safe distance.
Simple!