At the risk of complicating the generally very good advice given above, I would add the following:
All guns now need to be shipped to the US and there are several good people who can arrange this for you: John Farugia mentioned above is one; PAR Freight and PDQ Freight who are both located near Heathrow and are both highly experienced with this stuff.
Pre 1897 guns are easy, they can be shipped without an individual UK export licence by anyone with a suitable UK Open General Licence and can be picked up from the chosen US International with a minumum of expence and fuss. Alternatively they can be cleared and shipped to you by a customs broker but you will pay for the service.
Guns made in 1897 and 1898 require an export licence from the UK and an 'End User Undertaking'. This doesn't really involve any expence but must be brokered by someone with access to 'SPIRE' the UK online export licencing system so probably some charges will be made.
Guns made after 1898 require the above plus a 'broker to clear your gun in the US plus an FFL to recieve it for you.
One thing that is not common knowledge is that as a 'occasional importer' the purchaser effectively becomes the importer rather than the FFL. Therefore an ordinary FFL can recieve the gun on your behalf rather than having to use an 'Importer FFL'.
A special Form 6 is issued in these circumstances which has NOT FOR RE-SALE stamped across it.
I have imported a 1920's shotgun to a client in Texas within the last few weeks and the charges were $250 for UK-US shipping and UK Customs procedures plus $323 for the customs broker including duty (at about 3.5% on $2500.
I hope this helps.
Toby Barclay,
Heritage Guns
