Although firing shorgun shells, a .410 pistol still falls under a Section 5 prohibited weapon. A good idea mind you.
You can be granted one on a normal section 1 FAC with a good reason.
13.20 Section 4 of the 1997 Act allows the
possession and use of shot pistols in calibres
.410 and 9mm rimfire, provided that such a
pistol is “subject to a condition that it is only
for use in connection with the shooting of
vermin” (see Appendix 3 for the exact
wording of the condition which covers these
circumstances). This exemption was intended
mainly for pest controllers who may need to
use a firearm of this kind in farm buildings,
farmyards and similar areas where use of
a conventional shot gun would be
inappropriate, for example fruit cages
or near release pens.