Which begs the question as to why you think a pump action shotgun would be any different to a traditional one
A pump action shotgun fulfils the same purpose with a greater capacity than two shots. All this means is that you can shoot more rabbits before having to add more shells. Although the only real saving is the carrying of extra shells in the gun itself rather than your pocket.
There are other advantages: one barrel makes aiming easier, only one trigger mechanism is simpler and more robust, the whole gun is more robust from not having to break open, the safety is likely to be more reliable and so on.
There are good reasons for owning shotguns and small calibre rifles for legal use in Britain, and the restrictions of their ownership reflect that.
It's much harder to claim that handguns are useful tools for legal use, so they re very tightly restricted.
Mass shootings are a rare event in the UK(2010, 1996 and 1987 were the previous ones), which suggests that the rules work well. Tightening the regulations even further probably isn't practical, although investigation of who they were recently applied to this latest gun owner would be sensible