Well, an update.
I had a very quick and helpful response from the local man at the Environment Agency. Basically, my application for removing crays for personal consumption has been turned down as the specific stretch of river I requested is a hot spot for the native crays (and that's obviously fair enough, the whole idea is to improve their chances so I don't want to tamper with that) - he did however recommend some specific stretches of water where the EA are aware that the signal crays have basically taken over. He said if I wanted to proceed with my application based on those stretches of water he would get the application through ASAP.
Very helpful, very quick, just a shame the river that is almost on my back doorstep is a no-go.