Some interesting comments for sure and some just simply not true or people are misinformed.
I am so glad I live in a constabulary area which has a very good HAD scheme,
All the HAD's are very experienced stalkers and deer managers who have been trained and assessed by police firearms officers and HAD assessors before they go live on call outs.
Once you have passed the assessments you are exempt of some of the deer act's that control normal stalking activities and firearms laws ie calibres and use of shotguns on the highway but only while being called out as a police volunteer.
With all due respect, and I am aware that this is your speciality subject, but I don't think you're correct in suggesting that it is a requirement to have passed an assessment before carrying out HD at the roadside.
It may well be a requirement if you want to be "on the list" of "approved" despatchers that the local police might from time to time call upon, but often it's local DMG groups that organise a volunteer HD scheme in a particular area, not the police.
Neither to I quite understand your comment suggesting that, once you have passed an assessment, you may be "exempt" from certain elements of the deer act. That cannot be true, surely? The deer act has clauses that cover HD, doesn't it? No need to be exempt.
Have a good read of the relevant section of "Deer: Law & Liabilities" by Parkes and Thornely. Everyone involved in deer management should have a copy of that book.
As far as I am aware, anyone who is suitably equipped and sufficiently experienced can carry out HD to end suffering. In fact, in walking away from such a situation, if you could have dealt with it but chose not to, you could be deemed to be responsible for unnecessarily prolonging suffering, which also carries penalties.
There is no restriction on what a shotgun can be used for, or where it can be used, so either that or a knife are the default tools. However, if the injured animal can be moved off the roadside and onto adjacent farmland there is no reason not to use a rifle. As I mentioned earlier, for the purpose of ending suffering, as far as I am aware (see Parkes & Thornely) it isn't neccessary to have the landowner's permission if it is believed that he/she would be in agreement. But the carcass ultimately belongs to the landowner, regardless of the circumstances of its death.
(Just for the record, I have HD listed as a condition for my .243 so I can use it if a casualty animal is mobile or for any other reason unapproachable, but on stationary casualties I will always use my .410 shotgun.
After my last experience using a knife for HD I think I'll give that option a miss for the time being, but I do know that my daughter uses a knife for dealing with roadside casualties, by going straight in to the heart).