What it means
Used for someone wearing a proper sour, clenched-up face, like they're furious at the wallpaper and disappointed in oxygen. It's a vivid British way to say they look deeply unimpressed, bad-tempered, or one comment away from biting someone's head off.
Usage examples
"Dave rocked up and realised it was alcohol-free lager. He sat there chewing a wasp all night, like the bar had personally betrayed him."
"He sat through the whole meeting with a face like he was chewing a wasp."
"One look at her chewing-a-wasp expression and we knew the news was bad."
"You could tell the rota had changed again because Sharon came in chewing a wasp before she'd even put her bag down."
"Bloke at the next table's been chewing a wasp since his fry-up turned up without black pudding."
Where it comes from
It comes from the older British put-down a face like a bulldog chewing a wasp. That line's been around in UK speech for ages, painting that tight-jawed, miserable, ready-to-snap look. Chewing a wasp is just the trimmed-down version, but it keeps the same sour little sting.