I did, call it what it is: a gas expansion chamber.
Here is a 300 page document with a list of the export controls (isn't Google great).
https://www.gov.uk/government/public...-authorisation
Moderators are controlled as sound suppressors for firearms of type ML1a, but airguns firing inert projectiles are specifically excluded from ML1a. So are rimfire guns. So my reading of this (I am not an expert but I do work under government rules for my job) is exporting an airgun or rimfire sound suppressors is fine from the UK end.
BB