Because the cable is obviously not 100% straight, it touches both of
the walls at various points.. Could this be a source of damp?

I will be putting some insulation into the cavity, but should be doing
anything else to protect the cables?

You may well find it bridges the cavity. It is usually better to chase the
inside wall and plaster over. If you must run in there, you should use cable
clips to fix to the inner (dry) leaf. The bricks are over 50mm wide, so you
can run the cable at any height. I'd suggest near the top where you can
swing the hammer for the clips. You must derate the cable for the expected
insulation, which may require a ring main to be run in 4mm (or even 6mm in
some cases) after the calculations.

Christian.