In reply to JJL:
As you mentioned, building astride the boundary will benefit you only if you have any intention of building a similar extension that could make use of the wall, so that's what I would be asking myself. Not really from a cost point of view, I don't even think the charge to enclose on the wall (which they have suggested would be waived) is normally that high? but more as Derek says, it would be a bit grim to build another flank wall parallel.
Maybe also worth considering neighbourly relations? I imagine they prefer to gain a little more space (basically from you!) and build astride the boundary. That said we always advise to build up to the line (not astride) because it seems cleaner.
I assume you are the owners and have rented the property to someone else, because the notice is served on the adjoining owner not the occupier.
Hope it goes well.