Legislation that allows councils and other public bodies to enforce various motoring-related contraventions is now a complete Dog's Breakfast, and in serious need of reform to make it fairer to the citizen and less of a Magic Money Tree for councils, but don't hold your breath waiting !
As you have found out, there is no mandated time period for service of a PCN in the Road User Charging regulations. However, councils are under a duty as public bodies to act fairly and in the public interest, deviating substantially from what is normal in the other regulations could be considered unfair, but only an adjudicator can decide based on the degree of unfairness.
FWIW, I don't think you'd win on unfairness, because your wife had until the 21st May to pay the charge, having been detected on the 15th, so if you took 28 days from the payment date, that would take you to mid-June, so they have taken some days over 28, but with no limit, I don't think an adjudicator would find this unfair.
Of course, that's my view, others may differ, so wait a bit to see what comes up, but don't miss the deadline for payment on the PCN.
