The traffic order is
The Bromley (Waiting and Loading Restriction) Order 2003 but I am yet to receive the amending orders for North Road.
Ultimately however the traffic order doesn't matter: there is an exemption to waiting restrictions for boarding and alighting, even where loading restrictions are in place. The only way to prohibit this is to create a no-stopping prohibition such as a red route, a clearway, a box junction, pedestrian zig-zags or school clearway markings, none of which are relevant here.
This should therefore be winnable on appeal as long as the arguments are made correctly, I will drop you a PM in case you'd like to be represented.
It would be useful to see the actual notice of rejection, but frankly at this point I'd recommend you appeal no matter what it says.
As an aside there is no right to an observation period, if there had been no exempt activity taking place the council would have been entitled to enforce an instant PCN, as there is no grace period in law. Observation periods only exist to reduce the risk of incorrectly issued PCN owing to exempt activity happening out of sight of the CEO, but if there is no exempt activity and the CEO takes his chances by issuing an immediate PCN, that is not a ground of appeal.