In order to allow parking off-carriageway, the council first have to pass a resolution to over-ride the 1970s London-specific Act that barred off-carriageway parking. If all this resolution does is list the streets where the off-carriageway parking is allowed, then you have an appeal argument, as it is the resolution that counts, not the sign. In most cases seen on this forum, the council refuse the reps, and then one h as to go to London Tribunals for an answer. I'm not an expert on this aspect of London-specific legislation, but I expect somebody will be on soon to take you through it.
Please post the back of the PCN so the text can be checked for fatal errors.