i agree...fight for it....just write a letter to the council and explain the situation and say you shouldn be paying the fine...done mention about being over the time in the 1st spot...
i go to uni and i have to deal with it everyday when i am there...big car park and when they chalk you, it takes 500m of driving to take it off...i was speaking to the ticket inspecter there and asked him about moving the car 3 spots down...they go thats illegal as they want you to leave the car park properly and come back in...(that will give enough time for the chalk to leave the tyre)
since you did that, leaving the car park and then parking on the street, you did the right thing...but unfortunately the chalk didnt come off and it was placed the side up where they mark it....so do fight for it....you shoudl get away with it...you didnt do anything wrong... and therfore dont have to pay for it...