The fence is not always an indication of the boundary line. Even reference to the land registry plans is not an absolute guarantee of the boundary line.
How would the neighbour access this strip of land if he has installed a fence? Would access only be possible via your land? He has no legal right of access unless it is stated in the title deeds.
It does not make sense to put the boundary fence up on his on land and not on the boundary line. Where was the boundary fence previously? It is also a rather strange reaction by the neighbour. By cutting the grass you are not claiming it as your own and if that was his concern then why not build the fence on what he believes is the boundary line.
If the neighbour is claiming the land as his then he is entitled to request that you do not enter up on. To do so without permission is trespass. All you can do is deal with anything which encroaches onto your land.
I am happy to assist further if you have any further details.
Do let me know if you have any further questions or queries. I would be happy to assist you further.
If not then please can I ask you to take a moment to accept/rate my reply. Otherwise I will not get paid for the time I have taken to consider and type my reply. Thanks.