Unfortunately not. The company refused to write me a letter saying that they won't be paying any charges or recovery.
@hirerspcn you said in post 7 that you have a scanned copy of the Enforcement Notice (you don't need a physical copy, in fact you don't need a physical copy of any document at any stage of the process), and in post 9 Hippocrates told you to make a formal representation and gave you some wording. You also have a letter of authority from the hire company which you posted in reply 5 above. So, have you made formal representations against the enforcement notice?
This is what the council website shows now:


As far as I can tell, as long as you made formal representations then all you need to do is wait for the notice of rejection to be issued. You cannot rely on the hire company to pass it on, so just check the council website once every couple of weeks until a notice of rejection is issued.
To get the PCN history, go to
https://islington.tarantoportal.com/PCNs and enter the PCN details, once you're in (and only after you've logged in) change the address in the address bar to
https://islington.tarantoportal.com/PCNs/PCN/KeyEventsOnce a formal notice of rejection has been issued an appeal can be filed with the tribunal because you already have the LoA from the hire company, so at that point there's nothing the hire company could do to stop you or to mess up the process. Even if they paid the penalty, you would still be able to appeal.
You also don't need to worry about not having sight of any documents from the hire company, if the appeal proceeds to the tribunal then the council will provide the full history of all correspondence via the tribunal portal, again this will happen whether the hire company likes it or not.