Hello and thanks for using Just Answer.
I am Al and am happy to assist you with your enquiry.
The Deeds to both properties more than likely show this entrance as a shared passageway with both parties having a right of way over it. It is also likely that each property will own half of the passageway each.
As such, it would be normal and usual for this passageway to be kept locked for security purposes. You would therefore be legally entitled to secure a lock on the door, provided you gave the neighbour a key.
If I were you, I would get your Solicitor to raise an enquiry with the Sellers Solicitor asking the Seller to confirm that they will either sort out a lock now/agree to keep it locked, and get an assurance from the neighbour that they are happy with this, or if the Seller will not agree to put a lock on the door now if there isn't one, that he at least obtains written consent from the neighbour that he will have no objection to you putting a lock on the door/keep the gate locked, once you have moved in.
No Seller wishes to lose out on a Sale, and I am sure the Seller will therefore assist you in this request.
If, in the unlikely event that the above does not materialise, you could always pop over and see the neighbour now, so you can see how the land lies- you could just say that you wanted to say hello as the prospective new owner, and then just mention the gate in passing.
I hope this assists and sets out the legal position to you.