I am not sure that there are any new restrictions imposed on the import of shotguns to the UK. In my travels back and forth to US shows, I have not come up against any (last trip to the Vintage Cup in September, next to Las Vegas in January).
However, there has been a tightening of the rules applied by the shipping companies in regard to firearms in any direction, international or domestic, and it may well be these new company rules and regs that you are coming up against.
Basically they have decided that guns and the security considerations that they entail are too much trouble and expense and so it easier to not be involved.
As I avoid shipping guns back to the UK, all my guns travel as checked luggage, it doesn't really effect me but I can imagine that without using air freight and an agent/customs broker on both ends, it is going to be fairly difficult but probably not impossible.
You should consult with JF as he may have a suitable route he can recommend.
Otherwise, it would be best to carry it yourself or find someone who can offer you that service.
