Whilst in Safeway this afternoon, I noticed a stack of button-badge-making machines (Bandai "Badge It!"; marketed primarily at children) discounted to £12. So I picked one up.
It uses proprietary blanks, which are slightly larger (3cm diameter) and somewhat more elaborate (and probably expensive) than the usual button badges (a Bandai badge consists of a metal part, a plastic inset and a safety pin which goes through the inset), though it came with 15 of them.
Next up: to print out some designs worthy of being stamped onto badges. Perhaps one of them will be a "No I Don't Want Any Skunkweed" badge to assist in negotiating Camden High St. untrammelled.