There aren't any regulations which govern local authority off-street car parks as far as I'm aware. Neither is it practical or proportionate IMO for every relevant article of an order to be stated within the car park.
Photos are not a legal requirement. In any event the council have provided clear photos showing the significant incursion of the vehicle into an adjoining bay. As photos aren't a legal requirement it follows that the absence of a photo of the noticeboard cannot be a defence.
However, given the authority's terse and incomplete response to initial reps I would focus on their attitude to discharging their duty and look for a procedural impropriety defence.
IMO, acknowledge that the car was astride 2 bays- give reasons as well if necessary- but make the point that the conditions of use displayed on the noticeboard were noted but as these did not refer to 'parking wholly within a bay' even less to the council's powers should a driver err in this way the driver did not feel it was their absolute duty to park wholly within the bay.
If the authority consider that parking in this instance gives them the power to demand a penalty then they must explain why this is not brought to drivers' attention at the site. Any response to these representations which fail to address this point must be incomplete and therefore a procedural impropriety.
OP, use whatever words you like but IMO:
Acknowledge that the car sat in 2 bays;
State clearly that the noticeboard was read;
State your argument as regards the penalty;
Require them to respond;
..and if the payment machine gives different conditions to those on the noticeboard, highlight this discrepancy, state that it is confusing and ask why those on the machine are not replicated on the board given that certain drivers are exempt from payment and would not as a matter of course consult the machine, therefore placing them at a legal disadvantage.
They'll be other comments, I'm sure.
