No duty is correct but there is a handling charge although this has a maximum of $25 if I remember correctly. However that does not get over the customs broker charges if one is required because either the local customs office insists or one has to get it cleared for you for practical reasons, like you live a long way away.
Then you have to get someone to ship it to you if you can not collect it.
It all piles up.
If your airline of choice will let you, flying over to collect it yourself can be much the same price! However, don't forget that you are going to need someone (a Registered Firearms Dealer) to accompany your new toy as far as UK customs and baggage drop (without a Visitor's Shotgun Permit you can't wander about with a shotgun in the UK) and someone to do the appropriate export entry for you, the latter costs around 75-100 currently.
