IMO, do not appeal. You don't have a full set of facts i.e. you don't have a PCN to review. As posted below, you are in an ideal position to test their procedures to the full, so don't drop out half way and potentially let them off the hook.
Post the receipt for your payment pl. if you redact any info pl tell us its nature e.g. your name and address, your VRM etc.
Facts:
PCN issued 3 July;
You have evidence that you paid the road user charge for the crossing in question on 29 June.
The charge certificate states:
'If you pay within Penalty Charge Road user charge Total to pay
14 days of service £105 £2.50 £107.50
If you do not pay within 14 days from the date of service you will get a court order. I wonder what an OfR would state?
You are an ideal guinea pig! Why?
Because you can wait for/there's nothing else to do until you receive the OfR and file a statutory declaration that you did not receive the PCN. We would then see what 'debt' has been registered by DART.
IMO, in general they are entitled to recover the road user charge but not as if it were the penalty charge i.e. not under the same procedure. Hitherto in the procedure it could be argued that DART are just the right side of the line i.e. the 'standard' PCN refers to 'penalty charge' increasing for £105 and that a CC will be issued. But with the CC it states in the context of 'Total to pay'
'If you do not pay within 14 days from the date of service you will get a court order.'.
For £105.00+ £10(debt registration fee), yes. But not £117.50, this would be improper. Using the adjudicator's language payment of the RUC is clearly an implied requirement when in law it may not.
The other issue in your case is that you paid the RUC before the PCN was issued which, if your receipt proves that this should be allocated to your vehicle in respect of this specific crossing, means IMO that no RUC is due. What they might be trying to do is to treat your payment as a credit against a future crossing and still demanding a retrospective payment under the CC.
IMO sharp practice at best, unlawful at worst.
Anyway, you cannot appeal a CC so pl post your receipt pl.
Do not concern yourself about an Order for Recovery. If you submit your Statutory Declaration in time(tick one box, easier than falling off the Dartford bridge) the OfR would be revoked, the CC cancelled and a new PCN issued. See the legal procedure set out here:
https://www.londontribunals.gov.uk/ruc/understanding-enforcement-process#sdBut it's your choice.