Mostly, yes! They use a very specific clay from a producer which went out of business a few years ago. They've bought up all the stock they can and use that clay for pretty much all of the character puppets, along with other materials. There was a great documentary on the BBC a couple of years back which went behind the scenes and talked about how they make and use the puppets.
There has since been another company that has been able to produce the same clay so its now less of an issue.
Was it this documentary?!
https://www.youtube.com/watch?v=f19hF7-nT8g
/s