Some quick research determines that not just the barrel is determined as a firearm. The Crown Prosecution Service guidance is below:
308, CA states that the component part of a prohibited weapon is itself a prohibited weapon. Although there is no statutory definition, the Home Office Guidance to the Police at paragraph 13.70 states the following:
The term "component part" may be held to include (i) the barrel, chamber, cylinder, (ii) frame, body or receiver, (iii) breech, block, bolt or other mechanism for containing the charge at the rear of the chamber (iv), any other part of the firearm upon which the pressure caused by firing the weapon impinges directly. Magazines, sights and furniture are not considered component parts.
Therefore a replacement frame, which this seems to be, would put this as a section 1 firearm and not therefore exempt under the obsolete calibre rules.
I'll definitely be returning it to the auction house for a full refund.