In the sense of 'I can't believe it!', the origin is uncertain, but it is probably just a euphemistic version of something more profane much as 'Cor blimey!' is a more acceptable version of 'God blind me!
One meaning of 'to jigger' was to make a series of rapid, jerky movements such as a fish might make whilst trying to escape a hook. As a result, it came to mean exhausted, tired out or 'done for'. There may just possibly be some connection between the two meanings..."Well, I'm done for!"