You cannot lie or mislead, but you are not required to incriminate yourself either. Here's what I would suggest:
Dear London Borough of Wandsworth,
This representation is based on inadequate signage, owing to the defaced signage adjacent to the parking bay.
I was visiting my elderly parents who live in Atkinson House and parked on Austin Road in front of Atkinson House, and I displayed the parking permit provided to my parents for visitors to park. (See attached permit).
As you can see from my attached photograph the pole (008) where I was parked the sign was defaced and not clearly visible. I have also attached a copy of the adjoining pole (009) where the sign is also defaced. I was therefore not aware that the permit could not be used where I had parked as both the signs on that side of Austin Road were defaced.
The evidence provided by Wandsworth Council traffic warden is that of a clear sign which is on another road round the corner of Austin Road (Astle Street) and not on Austin Road where I parked my car. The pole photographed by the Traffic Warden is the pole on Astle street and is clearly numbered as 010. If you zoom in on some of the evidence photographs provided by Wandsworth Council one can see the defaced signs in the distance.
The contravention therefore did not occur as the bay where the vehicle was parked was not properly signed, it follows that the PCN must be cancelled.
Yours faithfully,
Take a timed / dated screenshot of the confirmation page.