I seem to have a strange structure to my wall. From tapping and using a picture nail, it seems like the structure behind the wall is like this, where the red squares are stiffer and the rest is plasterboard: 
I've tried drilling into these stiffer structures and it seems to just be plaster but I meet resistance at about 3cm - possibly metal, I'm not too sure. Any suggestions? My TV mount is a standard flat one, but without a vertical stud, it's hard to know what to do.
Could be metal. Either metal studs, or you happen to be hitting metal plates used to protect wiring behind. I doubt you have THAT much wiring, so it very well could be that your wall is built with metal studs.
Could be lath and plaster, depending on the age of the house?
The wood laths (or is the plural still lath?) are run across the studs, and studs can be irregularly spaced if it's an old house.
If this is just a drywall wall, then you might want to just cut a hole in it so that you can see what's going on structurally. You may then need to mount plywood to span the distance between studs so that your mount can sit on something solid - described here Can I hang a TV with one stud and drywall anchors?
