In the US, those are called fire blocks or something similar. They are not structural members. They are intended to slow down the spread of fire through walls.
Interestingly, although clearly talking about the same thing, the
Wikipedia article for noggins says that they are structural, and doesn't mention the fire thing.
As such, you should be able to drill through them without a problem.
Not without dismantling the wall, though (or, at least, cutting drill-sized holes in the plasterboard/drywall above each noggin, and patching them up again with more plasterboard), which is what Andy was probably hoping to avoid.
Sadly that does seem to be the best option, though. All trunking is ugly. The only other option (if you don't mind playing fast and loose with minimum bend radius requirements) is, if the room is carpeted, feed the cable round under the edge of the carpet between the gripper and the skirting-board. This doesn't deal with up/down cables, though. I got my Ethernet from upstairs to downstairs in a small cavity between the staircase stringer and the wall.
Peter