So let's get this right.
You had a perfectly good permit valid until the 8th. YOur new permit commencing on the 9th arrived on the 6th , and instead of replacing it in the car when the old one ran out, you put it in the car, and threw the old one away. So do the paper permits have a start date on them ? Also, I presume this swap-over practice has been going on for a long time, since 2011 ?
So have you submitted representations yet ? If not, I suggest you submit reps based on the fact you have always swapped over the permits as soon as the new one arrives to avoid forgetting about it. Point out you have been a resident since 2011, and have never before received a PCN for swapping the permits immediately. Post up their inevitable rejection when you get it. I you could post up the actual permit, it would help. Redact the reg number if you want, but it's not important.