Presumably your local police cleared this arrangement in the first place, in which case writing your name on your ammo boxes seems sufficient.
However, nobody can rely on the police to know the law and just because Plod A said something was OK doesn't mean Plod B won't be a dick about it and penalise you.
Why don't you just buy your own ammo safe /locked box and use that? My force is content with a £10 locked cash box bolted in place. (Ot at least, they have been for the past 20odd yrs.