Thanks, the 2nd URL shows some cheaper replacements.

but this

3) Or exactly how the lock barrel actuates the lock mechanism,
I can't for the life of me see how it does it, as the barrel end
doesn't engage the slot in the lock actuator, and there's no pins
etc that I can see to move it ?

Could do with an explanation, as even if I buy new cylinders, I don't
see how they'll work !

Unless something vital has pinged out .. but I was very careful when
dismantling ..

I suspect someone bodged the lock by leaving one of the securing screws
for the barrel proud, which has eventually snapped off, so there may be
something missing.
goes off to search for an exploded diagram ...

Cheers,

Paul.