Is this before you have started the rewire, or are you in the middle of it?
If the fan was not working, would it not have been better to test for voltage at the fan terminals, and also to test for resistance through the motor?
Anyway, if you have had power on which you must have because you say you were testing why the fan wasnt working, then if there really was continuity between live and neutral then would it not be tripping the RCD all the time? You cannot possibly have tested the main incomer on the cutout side??
if you have done the rewire and you do indeed have a low resistance between live and neutral then i think you need to check over your wiring very carefully or get in a pro. I would be asking why is the power coming on at all if there really is continuity between live and neutral, and you have fitted an RCD protected consumer unit.
Even on an old fuse based consumer unit, if you short out live and neutral, then the fuse blows almost straight away. What resistance reading are we talking here? 0.1 ohms or larger?