Why We Bother Checking
Unlike allergens, there's no established evidence that GMO ingredients pose a health risk, and major food safety bodies, including the FSA, treat approved GM foods as safe to eat. This isn't really about safety concerns for most people who look for this badge, it's about personal choice. Plenty of people simply prefer to avoid genetically modified ingredients, whether for environmental reasons, general caution, or just personal preference, and that's a perfectly reasonable thing to want clarity on.
The tricky part is that GMO status often isn't obvious from an ingredient name alone. "Soy lecithin" doesn't tell you whether the soy was GM or not, which is exactly why this needs actual sourcing information rather than a guess based on the ingredient list.
For the UK's official position on GM food regulation and labelling, see the Food Standards Agency's guidance on GM food.