Hollow walls in the UK usually (AFAIK) have horizontal noggins that stop you from passing a wire up a wall behind the cavity like this. I'd also say that a wall filled with insulation is a well constructed one, not a bad one!

Life is *so* much easier if you have a void under the floor or live in a bungalow

I managed to do some extensive cat5/alarm wiring by hiding it behind coving. You can also drill a small (20-30mm) hole in coving and use rods to push it through and then just plaster the hole.

I'd attach piccies but you can't see anything