There are
two 'No Left Turn' signs with a board below that gives times and exemptions, one each side of Finchley Road as you approach Pattison Road: -
https://maps.app.goo.gl/w4L4P3CoAoG5AQxP9So no sign is needed at the entrance to Pattison Road, and your PCN is for turning left inside the restricted hours. The sign banning vehicles over 18 tonnes is a separate restriction, and irrelevant to your case.
Assuming GSV of June 2022 is still the current view of the signs, in my opinion you really don't have much to use to form any representations, I'm afraid. There may be a technical appeal related to the PCN content, or Barnet's management of the enforcement process, so wait a bit to see what comes up, but don't miss any final deadlines for paying or reps on the PCN.