Car towed away with no time given to pay issued PCN?

[Morgentau]

I've been quite surprised not to find my car where I left it on Sunday morning..

Guilty I am - parked on a double yellow at the end of the street where there is no traffic on weekends.

I rang Trace and went to collect my car from the compound they keep towed cars, at Limehouse on Commercial Road.
Paid everything they wanted, e.g. £200 for car release and £65 PCN fine.

The question is - I have been told they got my car around 10:30AM and the PCN was issued around 9AM.

Car towed - 10:30AM. (told that on the phone by towing company, no written evidence yet)
PCN issued - 9AM.
I came to release my car - 2PM. (got all evidence of payment)

So I think Those guys towed the car and issued the PCN almost simultaneously!

My point is - any chance I get something back if I appeal?

Any suggestions on building a firm evidencial appeal please (Tower Hamlets Council)?
I'm so gutted of losing £200, this is unfair - I would be quite happy to pay the PCN £65 but not this!