RT,
Assuming GA in a private G-reg:
Don't just chuck your scattergun on the back seat. It should be unloaded and in a locked case, attached (even temporarily) to the aircraft (for instance by means of a cycle lock). This also ensures compliance with part 2 of the security condition on your SGC or FAC.
Section 20 of the Firearms Act 1968 effectively requires that you should have PPR so that you are not "a trespasser", but you are under no obligation to disclose the nature of your cargo to any third party.
Ammo is a different story; up to 5 kg per pax is allowed in checked baggage, whatever that means for a light aircraft with no pax...
How much of the above is practically enforceable may be a matter for others to judge, but licensed gun owners are, in principle, law-abiding folk.