Nevertheless how should I go about making my case for the adjudicator as you describe? Is there any case law
Appealing to the adjudicators, (in your case the Traffic Penalty Tribunal), is the last stage of the enforcement process. You can only appeal to them if you have had representations to the council refused. There are two stages of submitting representations to the council, (1) an informal challenge against the PCN and (2) formal representations against the Notice to Owner, this is sent to the vehicle owner when either no payment has been received for a PCN, or and informal challenge has been rejected, and no payment made.
We always recommend OPs (original posters) submit an informal challenge first. This gives time for investigations to be made concerning the alleged contravention.
As for "case law", the process is under the civil law, and there is no "case law" as made in a court of record, but each tribunal, (London has its own, BTW), must keep a Statutory Register, but each case turns on its own circumstances. An appellant can cite other cases similar to his own that have won, but it is not case law, therefore it can be ignored by an adjudicator. In addition, only the London Tribunals register can be searched, the one at TPT is not available for searching on-line.
Anyway, with the above out of the way, your case looks as it it should win at adjudication, because none of your car is over the dropped section, and only intruding into the sloped section by a few inches. The contravention is stated on the PCN - "parked adjacent to a dropped footway". The statute is "lowered to meet the level of the carriageway". Lots of councils argue blind that the sloping section is part of the dropped footway, but adjudications over the years show that adjudicators don't agree with them. However, as most people just cough-up when representations are rejected by councils, it is difficult to really determine how common this sort of thing is.
Anyway, best now for you to submit an informal challenge on something like the following lines: -
Dear Sirs
Re PCN <PCN Number> dated <dd/mm/yyyy) served at <hh.mm> at West Street
I deny responsibility for the PCN penalty above on the grounds that the contravention did not occur.
The photographs taken by your CEO show that the car is not intruding into the dropped section.
Please therefore cancel the PCN forthwith.
Yours faithfully
Post up their resp;onse when you get it. Don't be shocked if all you get is a Fob-Off letter of refusal. Councils ruthlessly game the system to maximise their income, and it works, because most peope then cough-up.