This is what the Environment Agency has to say about trapping.
Regulation is needed:
(a) to protect our native White-clawed Crayfish;
(b) because the traps and fyke nets commonly used to catch crayfish are "Fixed Engines" as defined by the Salmon and Freshwater Fisheries Act (1975); unless authorised by byelaws, the use of these instruments to catch crayfish is an offence under Section 6 of SAFFA (1975). Therefore, while fishing for crayfish is legal, unless crayfish traps are authorised by byelaws, their use is illegal, even where they are used within a site registered as a fish farm.
I guess what they are saying is, it's not illegal to catch them, but you will need a licence to take them, and that's where we came in.