I can’t think of any specific examples, but it’s usually in the delivery. “deadpan” is what they call it. They say something funny without changing their facial expression, except for one little clue that maybe they’re joking. Raising an eyebrow, curling one part on of the lip up. It’s like sarcasm but it’s not as obvious as sarcasm.
I looked up British dry humor under google images This showed up.
If you look at his eyebrows, they’re raised a little. You can see the creases in his forehead. But he says the words perfectly seriously, maybe changing the intonation slightly but if you weren’t paying attention, you might not realize he made a joke.