Hi, Jack.
Great post, mate and terrible luck!!
The bit that's broken's the cocking shoe (OOO-ERRR!!), the linkage sits in it and it slides up and down the cylinder as the barrel's opened and closed. When they break they tend to just fall out of the wider part of the cocking slot at the front of the cylinder.
It's about the only weak part on HW springers, I've changed a good few over the years.
Easy fix. New shoe, tap out the pin that holds the linkage to the barrel, place the shoe into the slot, engage the end of the linkage to the shoe, line up the linkage with the barrel then