Your laws in Aussie are prob very similar to NZs.
If you get struck from behind, ie, nose to tail accident, the rearmost car is almost
always held to be at fault as they have failed to stop in the clear distance ahead
So unless someone comes up and says that you were reversing back up the road , you should be in the clear there
You do need to report it asap to the Police
If the Police prosecute the taxi driver, I am guessing they may be able to ask for reparation to cover your damage
so its worth asking them about that and if they can ask for reparation, get a quote asap to give to them
If the taxi driver says he has no insurance coverage, the company he works for may have some coverage