All this talk about "needing" a pistol is kinda misleading IMO. The concept of "need" does not feature anywhere in the legislation, only the concept of good reason. Good job too I think!
The only people who really NEED any sort of firearm are the ones who do it for a job full time or the ones who have their own ground and cant get access to an estate rifle.
Recreational stalkers could use the estate rifle on a paid outing - no need to own a firearm yourself surely?
Target rifle shooters can use club guns - I've been shooting .22 at 25y for many years and still dont own my own .22 target rifle, and a number of other people at the club do the same.
If you can clay shoot at a large establishment like Bisley or West London you dont need to own a shotgun either - They have plenty you can borrow.... And even some of the small 28 day-er shoots have shotguns you can borrow, albeit not enough to supply 100 odd people at a time but thats by the by.
And as for travelling abroad? Nope, most outfitters can supply guns locally on the ground. Kiss goodbye to your .375's and upwards..
Personally I think we need to be careful about saying who "needs" what. If you've got good reason as per the law, meet the licencing conditions and can afford the kit fill your boots I say.
Our syndicate ground in Scotland has hugely thick sitka and spruce plantations all over the place - I personally would struggle to walk between the trees with my jacket on up there, never mind carrying a rifle as well.
I can totally see a handgun being about the only viable option tracking and dispatching a wounded deer in there, and if you want to go in after a wounded and angry 25 stone red stag with just a knife then you're a braver man than I... Take a few smoke grenades in with you so you can signal your location once the stag has turned you inside out with its antlers and we need to get the paramedics in.
To answer the OPs question - all you can really do is apply and see what gets said. I cant quite find the section in the guidance but as I recall it says something along the lines of "each case will be taken on its own merit and the fact that someone else in the area has been granted authority does not mean that another person should be."
There is some good guidance from BASC here under the humane dispatch section -
https://basc.org.uk/firearms/guidance-and-fact-sheets/