Very rough pub-maths answer: a lot less than people think, but not zero.

A normal charcoal BBQ is basically a small, crap combustion chamber. You’re burning mostly carbon, with a bit of hydrogen, oxygen, ash, binders, moisture, and whatever fat is dripping off the sausages. In perfect combustion most of the carbon goes to CO₂. In real life you get incomplete combustion, so some comes out as carbon monoxide, plus particulates, VOCs, aldehydes, PAHs, nitrogen oxides, and general blue-grey garden filth. Say a BBQ burns 2–3kg of charcoal. Depending on airflow, temperature, fuel quality, and how much the lid is being opened every thirty seconds by someone called Gary, you might plausibly be in the hundreds of grams of CO per session rather than kilos.

Scale that up. If a few million households fire one up on a hot weekend, you’re probably talking low thousands of tonnes of CO across the UK. That sounds massive, but once it’s diluted into the boundary layer over an entire country, it’s atmospheric noise compared with road transport, industry, domestic combustion, shipping, fires, and general background oxidation chemistry. The nastier bit is local exposure, not national atmospheric loading. Stand in the plume and you’re breathing fine particulates, soot, hydrocarbons, acrolein-type nasties, PAHs from fat pyrolysis, and a bit of CO from oxygen-starved combustion. Put the thing in a tent, garage, shed, doorway, or under an awning and the CO stops being trivia and starts being a Darwin Award submission.

So the boring answer is: BBQ season definitely adds a measurable little burp of carbon monoxide and smoke chemistry, but it’s not meaningfully changing the UK atmosphere. It’s mainly a hyper-local air quality problem caused by millions of tiny inefficient carbon fires and people burning meat in flip-flops.