Not sure what you are getting at LL.
If it isn't registered it means the Land Registry don't know who owns it - so there is no point in talking further to them. However you are right that it doesn't mean it isn't owned - it could be owned by someone who is sitting on original deeds to the land.
Either way, there is absolutely nothing Maz can do to claim the land legally. You either have to find the owner of the deeds (if he exists) and buy it, or you just fence it off and sit and wait - for 12 years. If a near neighbour is using as a cut through, you might get complaints.
If you are bold enough, just fence it off and tell enquirers that you have bought it - that's why you fenced it off. It might pay to be bold. The worst that can happen is the actual owner turns up and you've wasted a few feet of fencing.
Lastly if this piece of land has been used by the public for over 20 years as a cut through, a public right of way may have been established. Once again the way to test this is to fence it off and see whether anyone challenges you.