I recently did some research into this and came up with a useful link.
Lots of ambiguity and lack of definition but useful reading for anyone supplying "game" in either fur/feather or processed.
One interesting bit was this: (caveat: you need to read the "exemption" part for it to make full sense!)
"You do not have to be registered if:
• you have a shooting/stalking estate (with or without a game larder) where all the in-fur/infeather game produced is either for private domestic consumption or comes under the
exemption for supply of small quantities of in fur/in feather game direct to the final consumer or
to local retailers.
It is unlikely that your Local Authority will require registration if:
• you shoot recreationally on other people’s land and have no game larder of your own.
However, you may sometimes shoot more than you can consume or supply onwards to final
consumers or local retailers on the day. As long as the journey is short enough to prevent carcase
deterioration and the vehicle is suitably clean and free from sources of contamination from pests,
animals, etc, and that the carcase has been examined by a trained hunter then direct delivery to
the AGHE by the individual recreational shooter is a sensible option. If you are able to show that
this is only an occasional occurrence then it is unlikely your Local Authority would want to register
you or your vehicle formally. Ensuring that your vehicle is kept clean on shooting days, free from
contamination and, where necessary, disinfected, will demonstrate ‘due diligence’ under the Food
Safety Act 1990."