One of my formative memories is watching the year 6s in the year above dress up as pirates (or maybe rats? it's foggy) and sing the song "it's tricky" as part of the plot.
While searching for the name, I saw someone talk about a pirate themed play called "pirates of the curry bean", but looking at the songs I don't think that's what my school performed. I don't know if anyone else remembers this one, or if our school was just on an inventive streak. We did have a Doctor Who themed play also, perhaps that was another invention.
What specific plays/parodies did your primary school do?