Free Traffic Legal Advice

I have just received a PCN for parking outside Kew Gardens on the street.
When parking, we looked out of the window and saw a sign directly opposite with the details of parking restrictions and a RingGo parking zone number. When I opened the RingGo app, the same parking code showed at the top, so I selected that and paid for our parking.
When we cam e back to the car, we were surprised to see we had been given a ticket. On closer inspection, I realised that the side of the road we were parked on is a different coded zone with one number difference. The prices are exactly the same. The sign for the zone we were actually parked in was about 50 meters down the road, whereas the zone we paid for the sign was directly opposite about three meters away.
How best can I go about appealing this? It seems really unfair as we did the right thing and paid. Ours is the black car in the picture, you can see the sign we used opposite.
Pictures here: https://imgur.com/a/pCUleQT
Location here: https://goo.gl/maps/QYi6fs7RLMWS3frFA

How long was your parking session for?

I did notice that afterwards, however we only parked for 4 hours so were still within the restrictions of both zones. We received the ticket about 5 minutes after parking, annoyingly we even saw the attendants but obviously thought we'd done everything right so walked away before they got to our car. We actually left after about 3 hours so didn't even use the full session.