Ask an Property Solicitor. Get an Answer ASAP.
A prescriptive easement does indeed "run with the land", so if such an easement has evolved, it benefit Z's land, which is now in your ownership.
The practical problem is proving to Y that this easement exists- ideally, you should have obtained a statutory declaration from X confirming his uninterrupted use of the private road for 20 years, or even better still, an application should have been lodged with the Land Registry claiming this prescriptive right.
I hope this assists and sets out the legal position.
Can I assist you any further?
Hi, Can I help any further? If not, I would be grateful if you could rate my answer, so I can get credited for helping you. Best Wishes Al