Punch and Judy

Punch and Judy was a traditional puppet show.

After the Endovorms killed several civilians in Trafalgar Square, a Punch and Judy stand was abandoned, with the fleeing puppeteers still wearing the characters. (PROSE: The Lions of Trafalgar)

When the Sixth Doctor commented that Astrolabus was mad, he responded by hitting him repeatedly with a puppet he called "Mr. Punch". (COMIC: Voyager)

The Eleventh Doctor used a Punch puppet when he destroyed the Ice Governess with his sonic screwdriver. (TV: The Snowmen)

Extraterrestrial Equivalents
When the Fifth Doctor was on Manussa trying to prevent the return of the Mara, Lon and Ambril observed a puppet show which strongly resembled a Punch and Judy show. Whether it was the result of cultural interactions with Earth is unknown. (TV: ''Snakedance)

Behind the scenes
According to REF: The Brilliant Book 2011, a non-narrative source, when the Fourth Doctor was trying to get rid of a Cybermat, the young Winston Churchill thought it was part of the puppet show he was watching.