This is not a Penalty Charge Notice under the decriminalised parking laws introduced back in 1995, it is an Excess Charge Notice, and the legislation is completely different.
I would strongly suggest you submit representations based on your narrative. Don't go in all confrontational, be apologetic. Clearly you were entitled to be in that bay, but of course councils are greedy for your money. There are still a few councils that operate this old and discredited enforcement process, but it's still legal, I'm afraid. If they reject your reps, there is no appeal process, they have to prosecute you in a magistrates court. It's up to them to do this.