The next step after the rejection, is to appeal to the London Tribunals,..
This comment has put you off, which is a shame because it's not correct.
The stages are:
PCN issued to the vehicle. This may be challenged. This is where you are.
If you submit a challenge no later than Friday 1 Nov. then the discount will be re-offered if you're unsuccessful.( it says this on the back of the PCN).
Any challenge you make before Sat.(do it online) is risk free.
Next stage - a Notice to Owner would be served on the registered keeper. Are you the registered keeper or is the vehicle perhaps hired?
Then appeal. But you're nowhere near this stage.