It's not clear from your picture which wire is broken.
If it's a primary (240 Volt) you are probably screwed as they are usually put on first. If it's a secondary, you may be in luck but be very careful doing what Andrew & DF96 have advised. I am in Southwest Sydney if you require assistance.
When soldering, you must be very careful not to damage adjacent wires or accidentally solder to two wires. A shorted turn is very easy to achieve, but I guess as the transformer is otherwise junk anyway you might as well take the risk.