I'm still struggling with the photographic evidence, both yours and theirs.
IMO,
There is a traffic sign which regulates a parking bay. In itself this has NOTHING to do with footway parking*, it regulates a parking bay. The default position is that the parking place(of however many spaces) should be marked on the carriageway. But there isn't one on the carriageway. Instead, there appear to be some white blobs on the footway.
The council's position is that there is a clear and properly demarcated parking place wholly/partly on the footway restricted to Resident Permit Holders **** which not only reserves the place to those holders but also allows parking on the footway. This is nonsense in as much as there's a single yellow line at the edge of the carriageway which prohibits waiting both on and off the carriageway, so it's not possible to 'park' anywhere!
To them if you're within the parking place you're OK, but if outside then you do not have an exemption from the footway parking prohibition. In a way it's their equivalent of Floor's Lava!
But IMO from all the photos it's impossible to see whether the parking place is correctly marked and that you were parked beyond its clear limits, thereby being parked in contravention on the footway.
Can you take side-on photos which capture the sign and these markings?
*- because it's not the sign prescribed for a parking place on the footway but simply one on the carriageway!
On the carriageway: item 4 in the Part 4 sign table;
This Instrument consolidates, with substantial amendments, the Zebra, Pelican and Puffin Pedestrian Crossings Regulations and General Directions 1997, the Traffic Signs (Temporary Obstructions) Reg...
On the footway: items 2,6,7 etc in the above.