"If the items protrude onto your land then they
constitute a trespass and that's all you need to concern yourself with."

I've been following this thread. I'm with Mr.Baker; it's your land and
the neighbour should have sought your permission before installing
anything on or over it. However, bear in mind that he might have been
misled by the installer (who should have known your permission was
required). Alternatively, if he is a devious type, he may have timed
the installation to co-incide with your absence. Did he know you'd be
away?

The 15mm pipe could be a condense drain from a condensing boiler, but
should then have been in plastic. I think it is more likely to be the
discharge from a safety valve. If so then it shouldn't discharge
anything in normal use, but if it operated it could discharge very hot
water. It would have to be terminated in a visible and safe place. A
termination over a passage is a safety hazard, if it is what I think.

I think I'd write a brief note stating that your permission should
have been obtained before these pipes were installed, that you have
not given your permission and that you would expect all further work
on the installation to be stopped until you have received written
details of the works for consideration. When you know what it all is,
only then could you consider giving permission.