They probably do, except they're mostly politicians nobody remembers outside the UK. It was cutting edge stuff back in the day. I remember their US special had a ton of Ed Meese jokes that would make no sense to a non-American or anyone born after 1970. Hell, the only joke I got was that his head was cubical.. literally a "block head".
This show always made me mad when I was little because it had puppets in it, and yet I didn't understand what the fuck was going on. So it was an act of betrayal by the grownups. Why would they make a puppet show that children don't understand? I hate grownups.