As others have explained, GE is of no relevance.
Customs lanes require self-declaration. You self-declare if there are items that aren't permitted entry to the UK, or if you have items subject to tax and duties. My understanding from the past is that snacks meets neither of those (unless they somehow contain meat, or raw fruit/veg material, etc, are extremely extremely expensive.). In other words the responsibility is on the traveller as opposed to the border agents.
The US is a declare everything edible kind of country and not comparable.