Brian Reay wrote:

A 'rigid' glue may break up under vibration.

True, but that would leave me no worse off than I am now and until it
happened I'd have a useable SDS chisel.

Can you not remove the chuck and get a replacement?

I did have a quick search but didn't find anything available. And actually,
with comparable brand new drills available from around £50 I think I'd
probably prefer to go down that route.

Thanks for the thoughts.