The rules about dates changed in the UK back in 2012 but nobody told anybody until several years later!
The old rules were that guns made before 1896 could be exported under an Open General Licence which only required one to keep records, not apply for an individual licence.
All guns made in 1897 or later needed an export licence and an application for an SIEL (Single Individual Export Licence) for those made in 1899 or later needed to be supported by an ATF Form 6.
Under the 2012 rules (implemented about 5 or 6 years late I seem to remember), usually referred to as 'PL9010', any shotgun (not a military weapon) made in 1889 or before doesn't need any kind of export licence.
Those made from 1890 to 1898 inclusive do need an export licence supported by an End User Undertaking but obviously no Form 6.
Those made after 1898 need an export licence supported by a End User Undertaking plus a Form 6.
There are no government charges for any of the above but they do take a few weeks to process, you have to registered with SPIRE and they occasionally ask you really stupid clarification questions.
Best policy is to smile and say 'how high'!
Note: the responsibility for proving the date of manufacture lies with the exporter, there have been cases where someone took an educated guess and came unstuck. Not a pleasant experience, I am sure! The customs have the final word and ignorance is no defence.
I believe there are still Open General Export Licences for more modern guns but that is a whole different story and I don't claim to know anything about them!