With a view inserting a helicoil as suggested by Brian I measured the brake rod and adjustment nut and it appears that mine are slightly different.
The rod appears to be 9/32″ and the nut 5/16″ (both have 26 tpi threads). Consequently, the nut, although slightly catching on the rod threads, slips.
The nut appears to be of original Scott design ; perhaps the rod was replaced at some stage – although all the other bits screw on tightly.
Does anyone know what size the nut should be?