It is a difficult one Lizzy. We had the same experience as you many years ago. We bought a house off a person who kept land at the bottom of the garden over 3 houses and 7 at the far boundary. We paid him £1 a year rent! The fence fell down and it became a rubbish dump for all around. We asked him to renew the fence and he said he didn't have to do this. In the end we bought it for 1K. It was hard hot work clearing it. Different days then. Lots of bonfires. We both worked shift type jobs full time. You could just ask for a strip to rent and just suppress the brambles and worst weeds and let the wild life enjoy....not too much work?

I think you may have to get rather more professional legal advice than we can usually give on here Lizzy. It may be that you are totally unable to do anything about it. It is very sad when this happens. One of my near neighbours has a large garden but admits that they only bought the house for the building itself and have no interest in the garden. They are now known locally as 'the dandelion people' but unfortunately when we took advice we were told that they could do as they liked and 'weeds don't need planning permission'. Your local council may have set standards for gardens so check with them if you don't want to go to a solicitor.

If the property is leasehold, there may be a clause in the lease regarding not being allowed to grow 'tares' (which means weeds). If you approach the new owner, they may agree to do something about it, but without a specific clause in a lease on a leasehold property, they cannot be forced to do anything at all on their own land.
You're right about the leaving it wild thing - there is a saying that every tenth garden should be left wild and untended for the benefit of wildlife, so having this derelict garden there is probably beneficial in that way. In terms of the invasive and pernicious weeds coming through to your garden, how about trying to negotiate with the owner to at least allow you access to perhaps clear, and keep cleared (with weedkillers if necessary) a 2 or 3 foot strip where their garden abuts yours, assuming they don't want to do anything about it themselves? That way, the benefit to wildlife is still there, but you've partially resolved the issue of invasion by unwanted plants.

I would be inclined to let sleeping dogs or you may find it is sold off and becomes housing?

As long as it doesn't become a dumping ground for rubbish I would try to ignore it. Maybe you could grow some rambling roses which would ramble across and hide some of it! You can console yourself that the patch must be valuable to wildlife, as you mentioned.

It is a problem when 'googling' this tricky subject to find there is not a lot to be done, apart from a polite approach and an offer to caretake with a safe guard you will not attempt to 'squat'. Hence our £1 rental set up by a solicitor when we bought the house. Once the fence went builders started dumping, as there was some access from a side road. It was a frequent issue in CAB too. Not a lot to be done. We were lucky as we sold later for a decent price.

Thank you all for your comments. Still inclined to let sleeping dogs lie, seeing as I do not have time to clear the land. I do spray the weeds encroaching on my garden with brushwood killer in an effort to keep them at bay so will continue to do so.