You've done well to get that far in your understanding.
An easement is the generic term for a right that one landowner has over another's land. There are other sorts of easements - a right to free passage of water or drainage, for example. So think of a right of way as an example of one type of easement.
Easements are not automatically extinguished over time. So whilst you may have obtained entitlement to claim and register the land as your own (have you succeeded in doing this?), the easement is still there over the bit of land you claimed.
It sounds like this is not a public right of way. In other words, it is just the owners of these specific bits of land with the easements in their land titles.
I reckon you cannot deny this new owner his right to go through there. You are entitled to block the access from the general public, but you are going to have to come to an arrangement with a locked gate or similar, to which he has a key.
I'm sure you can use your powers of persuasion that it is in everyone's security interests not to have general access to anyone opened up again.