I used to operate to LCY - maybe I can put some of the stories to bed.....
Aircraft types, operators, and individual pilots have to be certificated to operate into LCY. The steep slope is a problem for some types in that even with landing config and thrust at idle, the speed cannot be kept under control. Embraer have a backup plan to install a ventral airbrake on the EMB-170 in case it can't make it in its initial form (two of the launch customers want to fly it to LCY).
I heard of a Dornier 228 operator which could only make the approach with the bleed air switched on, sapping a little extra from the engines, slowing them down a little. Don't know if thats true, and it possibly related to the early days when the slope was 7.5 degrees.
Obstructions are the reason for the steep approaches, never heard of proximity to LHR as a reason. Canary Wharf is about a quarter mile south of the 10 approach, and you pass it with about 800 feet to spare if I remember correctly. Another big one is the Millenium Mills warehouse at about half a mile range, just a couple of hundred feet south of the approach.
Fs747pilot your theory is interesting; having seen the view in the photo a number of times myself, I'd say the camera was about a mile out or less, putting him at about 400 ' above the airfield. The PAPI lights will show the same gradient whatever the distance.
Theres no parallel taxiway to backtracking for take-off is necessary, but this isn't unique to LCY. Departures are in either direction.
Firm landings are likely because pilots don't have the usual luxury of being able to float down a long runway trying to impress everyone with a greaser! There are various touchdown zone markings, and if you're not on the ground by them, its a go-around.
The slope is indeed 5.5 degrees, and looks pretty hairy the first few times. To a pilot accustomed to the standard 3 degree slope even a slight difference (say 3.2) is immediately apparent, and 5.5 looks very different indeed. In the early days it was 7.5 degres and Dash-7s were the only type allowed in. One made a demo visit before the runway was built, landing on the cleared dockside.
At the west end of the apron a curved line can be seen in the concrete, which is the outline of a former dry dock which previously occupied the present apron site.
A locator approach was mentioned in an earlier post. When I flew in there there were only ILS and Localiser approaches. With so many obstacles the minima for a locator approach would be so high it wouldn't be worth it!
Regards - Musang