There are a number of Notifiable Diseases in the UK which apply to deer, see below. Most are extremely rare, some have never been reported in the UK ( with a * ) so may never be encountered.
The main disease that applies to us as deer stalkers is Bovine TB.
However in many areas APHA will not be interested in cultivating a sample and therefore visiting a location if confirmed. As of (at least) July ’18, they are only interested in captive deer with suspect bTB.
With wild deer, only interested in suspects from ‘bTB hotspots’, as I found out when I called the national contact number, 03000 200 301; they didn’t want to test my suspect muntjac from Berkshire.
Seems to me you still need to call APHA to cover yourself and to find out if a suspect wild deer was shot in an area of bTB interest, which then means sending in a sample.
Notifiable diseases applicable to deer
Anthrax
Bluetongue
Bovine TB
Chronic Wasting Disease*
Epizootic haemorrhagic disease*
Foot and Mouth Disease
Rabies
Warble fly (England and Scotland)
Taken from:
Notifiable diseases in animals