Am I likely to damage anything if I really get brutal, or is there any way
of freeing it up? Alternatively, I presume I can turn off the cold water

Yeah. Probably a gate valve. These are almost guaranteed to seize within a
few years. I had to replace mine a few weeks back for the same reason. Don't
get too brutal with a tank full of cold water to come out of the broken end.
Drain the cold tank and replace the valve. I've started using lever ball
valves instead of gate ones. From what I can tell, they are what is used in
Europe.

Christian.