It shouldn't actually be a problem if the gun is actually over 100 years old. Under UK law new made guns cannot be considered antique even if they are muzzleloaders, but a percussion shotgun should not even require a shotgun certificate. There are additional licenses needed if you want to shoot it but that isn't an issue here.
I've sent guns via UPS, FedEX and postal service... etc...and it can be a $#@* shoot getting the right person in those organizations who knows their own rules. I usually fill out the customs declaration very precisely and truthfully but in a way most people will not readily understand... i.e. instead of "old shotgun", "16ga Manton dbl Antique over 100 years old". The recipient will have to pay duty and probably have a headache with the UK customs but there is nothing illegal about such a shipment. It would probably be a big help to mail to a licensed dealer in the UK just like our FFL works. They will be in a better position to explain to the customs people what is legal and what isn't.
