the characters are apparently descended from Commedia, funnily enough.

Not improvised, no. But over the course of the run, the script tends to be deviated from more and more! There aren't standard scripts, but traditionally, there are only about 12 stories that are used (though there are some new ones that have been incorporated in recent years). They're mostly based on fairy tales.

You have stock characters and a kind of stock structure, with "set pieces" that turn up over and over again. But the interesting thing is that they've always been popular entertainment, incorporating poplar culture entertainers and references. So despite the fact that references to TV shows and pop culture characters is sometimes frowned upon by "purists" (including me), it's actually quite true to the spirit of the panto tradition.