I'm very surprised they towed the car away when you are a resident and permit holder, and also merely for non-payment. A PCN would have sufficed, so this is exceptionally venal and rapacious treatment.
If there is any good news, it is that you have already now paid all there is to pay, so it is a no-brainer to take this rapacious council all the way to London Tribunals. If you win you get all the money back although I doubt you'd get that, but possibly the tow fees as this seems a disgracefully disproportionate penalty for what is a minor parking error.
So your first step now is to submit representations stating, essentially, what you have told us, and point out the the penalty seems very disproportionate for a simple parking mistake, bearing in mind you are a resident and a permit holder. Post up their reply when you get it