Many thanks to everyone for the new replies; apologies for not responding to
every one individually.

As several people have said, the crux of the matter is the accurate
definition of the exact boundary line between the two properties. It's not
practical to measure the full width of the combined bungalows and divide by
two, but given that when built they were mirror-images of each other, it
seems reasonable to use the two rear-wall window openings closest to the
boundary as indicators, and to halve the distance between them. This, I
believe, is what my neighbour has done (relying on photographs of the rear
of the properties before my rear wall was demolished and rebuilt with
different windows).

By that criterion, the side wall of the ground-floor extension is clear of
the boundary line. The cladding on the end wall of the dormer does make it
wider than the lower wall but it's ambiguous as to whether or not it takes
it across the line. The architect (working from pictures at the moment,
though he does plan to make a site visit) says that it doesn't seem to; I'm
not sure one way or the other; my neighbour claims that it does.

He also claims that the entire construction is closer to the boundary than
is shown in the drawings and that if it had been built in the right place
then the overhang wouldn't have happened. The builder is calling tomorrow
to talk about this aspect.

And that is the situation in a nutshell.