I'm gonna say not illegal i did find this online section 12 may be a little out dated but i guess its still an active law:
Section 12 of the Licensing Act 1872 provides offence for being drunk with a loaded firearm; “Every person who is drunk while in charge on any highway or other public place of any carriage, horse, cattle, or steam engine, or who is drunk when in possession of any loaded firearms, may be apprehended, and shall be liable to a penalty not exceeding forty shillings, or in the discretion of the court to imprisonment for any term not exceeding one month”.
NOTE: Whilst the law prevents the police from prosecuting you for having an “unloaded” firearm in a public place, the police may conduct a suitability review where they believe you are intoxicated and deemed not to be in control. Each case must be taken on its merits and BASC advises never to over indulge.
Section 25 of the Firearm Act 1968 makes it an offence to; “Sell or transfer any firearm or ammunition to, or to repair, prove or test any firearm or ammunition for, another person whom he knows or has reasonable cause for believing to be drunk or of unsound mind”.