Don’t know the area that well but have ridden around there a few years back
Just a small point is it full on cheeky or did someone once say ‘ah go on you can ride through’
looking at the sales details it states in the general conditions of the sale previous agreements for easement and crossings will still stand or something to that effect
If the land is leased to natural England surely it’s there job as the lease holder to police ‘there’ land not the ‘owner’
Nearly all the best riding spots from my childhood are gone or fenced off now but I still go there when I can and would argue till I was blue in the face that I have ‘earned’ the right to be there as I care for the area I guess you feel the same
Good luck