I'm pretty sure that would be illegal in the UKicon - a shotgun firing 'slugs' is classed as a 'firearm' and would need to be on my FAC (Firearm certificate), as a shotgun its on my SGC (Shotgun Certificate)
There is a maximum pellet size to be classed as a shotgun - I could be wrong but I thing its SG or maybe AAA size.

Although my son has a BP 50 cal on his SGC the only difference is that the 410 would be fired from a 'cartridge'

Tricky one that !!!!