I can see the use for carrying one in addition to a rifle if used to dispatch a wounded animal at close quarters, especially in dense undergrowth where a scoped rifle would be difficult to accurately aim at an animal moving and thrashing around for a follow up shot. Over penetration and ricochets at very close range on hard stoney ground is much more likely with a centre fire rifle calibre bullet too.
A lot of police forces are in truth, very reluctant to issue you with the required permission to own a pistol / revolver for HD purposes whether you are legally entitled and can provide good reason or not. It pretty much depends on how your own force views it. The main reason actually appears to be the possibility of the pistol ending up in criminal hands through a burglary etc, although the evidence to back this up doesn’t really hold water and you could say that the same risk applies to any rifle or shotgun.
The recommended route would be a smallish 357magnum / 38 special calibre revolver. These are pretty much limited to a two shot capacity now for this purpose, so the rest of the chambers in the cylinder have to be professionally restricted to limit the capacity to two shots. This again is aimed at the possibility of the pistol getting into criminal hands. A semi auto pistol with a restricted magazine is unlikely to be granted due to the possibility of obtaining unrestricted magazines, which obviously hold far more ammunition.
I have extensive experience shooting my own revolvers and semi auto pistols from the pre 1997 ban pistol shooting days. This was at targets / steel plates etc. The red tape surrounding ownership, especially in my area prohibits me from applying for one though I did consider it at one time.
A thread like this usually ends up with the majority of replies stating that you don’t need one, a 410 single barrelled shotgun is better, pistol calibres are ineffective etc etc.
Many people replying, actually have zero experience with them and seem adverse to anyone owning one.
It is not clear if you are seriously looking to get one or not but if so and can provide a good reason for one, run it by your FEO to sound out the possibility of being granted permission for ownership. You will soon know if it is likely or not.