You have not posted either of the PCNs, so we don't know what Act it was served under. So please help us to help you by posting the documents.
It seems the PCNs were for parking, and if so, this is under the Traffic Management Act 2004. For PCNs under this Act you can submit a Witness Statement against the Order for Recovery, but there are only a limited number of situations you can report. The form is Form PE3, but looking at your narrative, none of them fit your circumstances, and you are dependent on the goodwill of Southwark, because you did not do anything after receiving their rejection of your reps. See here for the form: -
Form PE3: Challenge an unpaid penalty charge notice.
You do not seem to have done anything at all about PCN PCN JK17298185, so the enforcement process will have run its inevitable course, but it would seem is now at the Charge Certificate stage. With no reps submitted, it's difficult to see this one ending favourably.
Unfortunately your story is an example of what happens when a PCN recipient doesn't respond fully to documents and lets things slide. Once matters get beyond the OfR stage, you'll be getting bailiff letters. The first is the Compliance stage, and adds £75 to what you owe the council.If the bailiffs visit you, another £235 is added on. These amounts are statutory, by the way. I'm afraid civil enforcement is as harsh as the old criminal law enforcement, and maybe more harsh when one looks at the sums that can accrue.