I think being pragmatic is the best route. £1K is a hit but as others have said, nothing compared to the grief of going legal. I would just go and see neighbour, and say that it has come to light that the previous works probably weren't to regs. Get confirmation there is no issue fixing to their wall on your side, and no cost to them, which will address the issue and all is good. If they don't agree, only then you can threaten a legal p*******g contest involving their satellite dish, soil pipes, PW dispute etc.