Firstly all the talk about it being an airfield is wrong, it is private land. Personally I wouldnt even describe it as an airstrip but actually its a field you happen to use for your aircraft, you can use your own land for any activity 28 days of the year without planning consent, bear in mind that is days per year if you happen to 20 flights per day that is within the planning law.
The people who stray off the public footpath are trespassing on private land therefore actually don't have to many rights if the land is signed posted as private land. Wether they get run over by a tractor or an aeroplane is actually their fault because they are trespassing.