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GOV.UK
Food and other necessary goods
This includes those involved in food production, processing, distribution, sale and delivery, as well as those essential to the provision of other key goods (for example hygienic and veterinary medicines).
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Stalking as a totally recreational entity, I can understand if it must cease for a period of time. However crop protection form an agricultural point of view is still part and parcel of food production, whether this is fencing off rabbits and deer or managing them by shooting. This is not about getting around the Government instructions but carrying on with your job (paid or unpaid) as part of 'agri-production' as per food production above.
Personally I feel shooting deer at the moment is fairly pointless as most game dealers aren't taking them and are probably on the verge of closing for the foreseeable anyway. Shooting the odd deer to keep them off a particular crop may be necessary but won't last for long as a solution and then you need to dispose of the carcass into an almost full freezer!
For me all my deer management is local, on my doorstep, and I don't need to come into contact with another soul so if required and legal under the current Government instructions will carry on but in a very limited capacity. As a registered food business I could process the meat following all food hygiene guidelines, then most probably give it away locally.
I am searching/asking for the official line on this and assuming I get an answer I'll post it.