I was rather hoping for a more definitive answer to this one. I have a similar situation.
In my late parents' house, which my siblings and I still own, there was a front wall between our neighbour and us. All the time I grew up it was accepted that, that wall was Mr. XXXX's, and the wall on the other side of the garden, between our other nieghbour and us, was ours. And so when this first wall started to need repair we hoped the latest owner would not let it get too bad and fall into our path.
Now I heard from my brother that the subject has been mentioned, and the present owners deny all responsibility claiming it is our wall. So it's the neighbours all the time I've been around, but apparently ours now it need money spent on it. Typical !