Wino,
As far as I can see, although passengers may carry firearms on an aircraft, they must be unloaded, and not in an area to which the passengers have access.
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Unless anyone can find different the Air Navigation order applies as follows:
Carriage of weapons and of munitions of war
46.—(1) An aircraft shall not carry any munition of war unless:
(a) such munition of war is carried with the written permission of the Authority and in accordance with any conditions relating thereto; and
(b) the commander of an aircraft is informed in writing by the operator before the flight commences of the type, weight or quantity and location of any such munition of war on board or suspended beneath the aircraft and any conditions of the permission of the Authority.
(2) Notwithstanding paragraph (1) of this article it shall be unlawful for an aircraft to carry any weapon or munition of war in any compartment or apparatus to which passengers have access.
(3) It shall be unlawful for a person to carry or have in his possession or take or cause to be taken on board an aircraft, to suspend or cause to be suspended beneath an aircraft or to deliver or cause to be delivered for carriage thereon any weapon or munition of war unless:
(a) the weapon or munition of war:
(i) is either part of the baggage of a passenger on the aircraft or consigned as cargo to be carried thereby;
(ii) is carried in a part of the aircraft, or in any apparatus attached to the aircraft inaccessible to passengers; and
(iii) in the case of a firearm, is unloaded;
(b) particulars of the weapon or munition of war have been furnished by that passenger or by the consignor to the operator before the flight commences; and
(c) without prejudice to paragraph (1) of this article the operator consents to the carriage of such weapon or munition of war by the aircraft.
(4) Nothing in this article shall apply to any weapon or munition of war taken or carried on board an aircraft registered in a country other than the United Kingdom, if the weapon or munition of war, as the case may be, may under the law of the country in which the aircraft is registered be lawfully taken or carried on board for the purpose of ensuring the safety of the aircraft or of persons on board.
(5) For the purposes of this article a "munition of war" means any weapon, ammunition or article containing an explosive or any noxious liquid, gas or other thing which is designed or made for use in warfare or against persons, including parts, whether components or accessories, for such weapon, ammunition or article.
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However, the ANO is a Statuatary Instrument, and can be ammended by the Privvy council (excuse spelling) which does not take an act of parliament, in other words the ANO could be changed in around 5 minutes......