Private fields are not illegal, but will have pitfalls
Discharging an air weapon within a distance of a public road is illegal (I can't remember off the top of my head but the middle of farm land is ok)
However - you become liable for allowing activity
If you are not the land owner / farm operator then they also become liable
Farms are not private - they are businesses, you instantly become liable for any one on site due to business. (Delivery / collection lorries, vets, joe public buying eggs etc)
You are liable for trespassers. Even if it is illegal for them to be there
Put up signs
Tape/Fence boundaries (beyond range and playing area)
Have up as much netting as you can get
If you get inflatables then you need to keep cleaning them and packing them away