I want to redeem myself from previous comment
"It is illegal to bring into the UK, sell, hire, lend, give or possess in private the following, unless a legal exemption applies:
swords, with a curved blade over 50 centimetres (with some exceptions, such as antiques and swords made to traditional or methods before 1954)"
And more:
Swords with a curved blade of 50cm or more may be imported where the weapon:
was made before 1954
was made by traditional methods of making swords by hand
is only available for the purposes of use in religious ceremonies or for martial arts
is for use in a historical re-enactments or sporting activity for example a martial arts demonstration for which public liability insurance is held
https://www.gov.uk/guidance/import-controls-on-offensive-weapons
Just in case buy with papers. And maybe join some nihonto association.