My guess is that the cables are the Raleigh-specific ones that have both ends (what do you call those thingies?) soldered on with the casing and adjuster unremoveable. The end hooks onto the Raleigh caliper and is not attached with a pinch bolt. Those will be hard to find! Your best approach is probably to find a donor Raleigh Sports (or Rudge or Humber) that has the correct brakes and cables. The "lesser" Raleigh brands like Robin Hood, Triumph, etc. will probably be equipped with more normal brakes, with pinch bolts. You probably need to pay attention to the overall length you need, too. Alternatively, you can switch brakes or make special cables yourself.
David Bean
Arlington, MA USA
beandk at are-see-enn dot com