How about using a small drill bit (or something similar) as a drift, put it in from the other side and try to line up on the point of the broken key, and tap it gently with a hammer.
Nick
Do not use a drill bit as they can be quite brittle, you do not want to add to your woes.
The lock is already s*****d, what else would you have in your toolbox??
All I am doing is offering ideas to try and help.
Nick.
I've tried poking various sharp thin instruments to try and push out the broken key. But I don't want to push too hard with it incase I break the lock. I've tried a thin bit of rigid wire but it only pushes in so far and I don't really know what I'm pushing up against, whether its the mechanism inside the lock or the key end itself.