Why can't you wait 4 months and apply again?
Damn, so close.
What do you use the land for, does any one else use it as well and, if so , for what purpose/
I have to pop out soon but will be back on the system later.
Do you know which part is your and which theirs what do the deeds and plans show?
It is difficult because you were aware when you bought it that it did not belong to you and could be used, albeit, that they misled you over how they intended to use it.
They were clearly clock watching in terms of adverse possession as they nipped in just before the 10 year limit.
If this affects other residents you can try to get letters of support on the basis that it is not necessary as there is another route, it presents a security risk giving access to the back of the houses. The noise potentially created could cause a "nuisance" . Object strongly to persimmon and consider getting your local MP, Councillor involved, contact a local freebie paper they are usually desperate for local stories to fill the pages.
It is not illegal as long as you are desperately sure of your ground.