The list refers to convictions NOT cautions, as determined in magistrates or crown court (in the UK). It does not include convictions classed as 'spent' under UK law.
So Capt Stable, if your conviction for possession of a shotgun without a licence occured such that it is not yet a 'spent' offence, you will indeed lose your entitlement to an airside pass, and as such potentialy your job!
There is an appeals proceedure and offences are considered spent according to the severity of the sentence, not the actual offence.