If you’ve recently moved in, you might not have received your copy deeds from your Solicitor yet (Land Registry are very behind and everyone demanding theirs is expedited).
Have a look at what you were sent prior to completion. Is there a mention of your property having a right of way/ access over this passage? The deed is called ‘official copies of the registers of title’. Sometimes these rights are contained in old transfer deeds - ‘e.g. all those rights granted as per a transfer deed dated 1885. Copy filed’. Your Solicitor should have brought to your attention that there was a right of way/access as that’s really standard.
If your neighbours go for adverse possession of the land - they can’t just say I locked it in excess of 12yrs ago and no one other than us has used it. They simply won’t get it on those grounds 😂 Land Registry make you work for your possessory title these days’. They want proof not say-so. It’s a laborious form filling, document swearing, receipts gathering, witness statement, photos, etc… - and I hope he’s got a receipt for the lock!
As mentioned by a previous poster - Google Earth is great for historic images and Land Registry accept them. It’s a bit tricky to find it , look for ‘historic’ on the drop down menu and you can scroll back in time. See if you can spot things going against what they say. How long did the previous owner live there?
If there is no right of way mentioned in your deeds and that land at the rear is unregistered then Land Registry won’t write to you. They might come down and do a site inspection though - and when they see your property, might start digging a bit.
What you could do is check Land Registry and search your post code. If you see something like ‘land on the south side of number 20’ that will tell you, they’ve got a pending application at the Land Registry and you could obtain a copy of their application and then object to it.
Or you could maybe speak to Land Registry and see if they will let you register a ‘caution against first registration’. Think it’s £40 to do that. Do this if you have a right of way in the deeds and they don’t let you have a key. It’s a great move on your part!
If you have a right of way noted in the deeds then they’ll not get rid of that - not unless you agree to extinguish it.
If you want you can send me a copy of the deed. For your own peace of mind you can black-out all identifying information eg names, addresses, title numbers. I don’t need this info to advise you (former property and property litigation lawyer).