Mike Dodd wrote:
Is it common for stud partition walls in relatively new-build houses to have
only vertical beams (apart from top/bottom, of course) thus allowing a
vertical drop of a cable?

No, uncommon I'd say.

You ought to be able to tell where the horizontal members (noggins) are
by tapping the wall; if not you can get electronic stud-detectors at B&Q
etc (can't vouch for their usefulness though!).

Even assuming there are noggins, it's not that difficult or invasive to
get round them; essentially you need to end up with a small hole in the
plasterboard above and below the noggin so you can get a drill through
the noggin. Afterwards the holes can be repaired pretty much invisibly,
(providing you don't need to wallpaper the whole room again!)

Suggest you search the uk.d-i-y archives via google for the keyword
'noggin' - this topic comes up here regularly.

David