I suspect Woozer is right, but I'm prepared to keep going with the free advice if it helps.
I still don't get the picture fully, but it sounds like you share a party wall, and for the first 2 storeys, both properties share this wall. More recently they have extended further up the line of the party wall, enveloping the hopper downpipe that was technically in 'their' part of the plot.
If that is roughly right, the Party Wall Act 1996 should have applied, but if the work is done it is somewhat too late now (hence my question about what steps you took at the time).
I still don't get the bit about which window of yours faces into their plot.
There are minimum distances involved in where boiler flues can be - I'll check them out and report back if it helps? Not figures I keep in my head.