IMO, you cannot appeal because you have not received a notice of rejection of representations, neither are you in time to make a statutory appeal but instead would be relying on the adjudicator's powers to register an appeal submitted late which rather presumes you know what this needs to include(which is reasons for lateness)!
If date of posting the NOR was 5 June then the 28-day appeal window opened on 7 June and closed on 4th July.
IMO, you should let the process play through i.e. Charge Certificate, Order for Recovery and then witness statement.
It's not your task to chase TfL, their legal duty is to consider and respond by post. Can we presume that nothing was included in your reps - which we've yet to see- regarding addresses for their response?
And pl get hold of their camera evidence.