What is virtually certain is that Derby council will not accept any reps, so if you want to fight the PCN, you will have to take them to the Traffic Penalty Tribunal with the full PCN penalty in play, but that is all, there are no additional costs whatsoever, and, of course, if you win you pay nothing.
The evidence of the contravention is the video, so if it doesn't show any signs passed, they must show that the signs were in position on the day of the contravention. Many councils make a complete mess of doing this, and the appellant wins, but a lot does depend on the adjudicator. As SFM says, photos of several years ago may not be considered good evidence.
Also forget the criminal test of "beyond all reasonable doubt"; it is the civil law test of "on the balance of probabilities" which the adjudicator will test the case against.