I'm no expert, of course, but I believe that being a sewer for both yourself and your neighbour the responsibility for its upkeep would lie with the water supplier.
That doesn't help with your wish to re-site it, though, I suppose.
It's uphill from us, so it seems just to be for the house behind us... at that point anyway.
Found an old planning application which I've added lines to.
If it does just serve the single house behind, would that mean any issues are the responsibility of them until which point we join?