I can only speak for the general opinion of my force, at the last point that I dealt with them.
Calibre seems to be a big deal. If the list says .30 for deer then they will grant a .30 for deer. In my case I asked for a .375 Winchester for deer and they said no. .375 is on the list for dangerous game so it's not suitable for deer. No amount of reasoning would shift them, even giving info on the energy levels etc from reputable sources which they could reference. In the next breath though, they gave me a .416 for boar. There is no list for boar so they don't have to adhere to it. At that point they seem to fall back on the fact that the smaller of the dangerous game cartridges may also be conditioned for use here once good reason has been established elsewhere - Gloucestershire read that as .416, but not .458.
The next step is to ask for the .375 Win for boar. They put AOLQ on everything anyway so the whole system is a farce. I could literally shoot a mouse with my .416 Rigby.