Hi Rupert (fellow Shefflad!!)
The non cocking problem could be a worn sear or possibly other trigger associated parts, it could also be that someone has messed with the adjusting screws and set it so fine that it simply won't 'latch' on..
I suppose another cause could be a worn piston rod (unlikely though).
I'm not familiar with a FWB action but i seem to recall that they are of a good design and reasonably easy to work on..
HERE is an exploded diagram of the Sport range so that you can see what's involved with stripping/rebuilding...
Another possibility is the trigger spring, if that's broken it would probably only be possible to cock the gun by holding the trigger forward...
You could try Hardys gun shop (Ecclesall road) for parts or Guns international (Stairfoot, Barnsley) depending where you are in Sheffield...
I would try to get an original Feinwerkbau spring though and avoid the harsh square section springs which could possibly earn you a stay at her majesty's pleasure
Good luck with your rifle
John