The council numpties seem to have been confused by the date on your PbP receipt, which has the date in an unusual order of yyyy/mm/dd, thus thinking it relates to 8th July, not 7th August. Can you post up the full PbP transation please. There is no time/date for the parking transaction itself, only the times for the actual parking. Was the session taken out late ? PbP sessions are downloaded to CEO handheld terminals; this is how they check cars that have no actual parking ticket.
If you are certain about the correctness of your case, don't pay, but register an appeal with London Tribunals. There are two things as I intimate above, (1) date format and council confusion, and (2) when was the parking session established, time and date.
PLease note that in paying to get the car released, you have paid all there is to pay, and would not have to pay the additional £65 at London Tribunals even if you lose.