Not something I normally advise but for the time & cash it will take you to bodge a repair, why not sell yours on eb@y for £5 "spares / repairs" and start looking for a used one (one of mine was a freebie the other cost £20, it's not worth spending hours trying to fix yours).
It's just a thought
Info for other readers - the keys on mine are rectangular section bar with teeth cut on each of the 4 edges, it's not a tubular lock
It's just a thought
Info for other readers - the keys on mine are rectangular section bar with teeth cut on each of the 4 edges, it's not a tubular lock