So, it turns out that most cask ale is not suitable for vegetarians, because isinglass (fish guts) is used as finings to filter the beer. Bottled beer is usually fine, since it's either cold filtered, or left to settle naturally. (I was surprised to learn that, since I always assumed cask and bottled beer was produced in the same way.)

Breweries who use isinglass claim that it's the only effective method to filter the beer. I wonder how true this is, especially since other breweries seem to have no problem producing beer without it.