Not sure if we have any European pilots on here, but I'll still take a shot in the dark.
On the approaches to London City, is there a procedure to disable the eGPWS? It seems that such a descent rate would spook it to the point of at least getting the "sink rate" callout. I know the terrain/obstacle floors are included in the enhanced database, but the sink rate call is not associated with any aerodrome area, just purely RA change.
I'm not a European pilot, but I believe I can answer the question (at least when it comes to the ERJ and Airbus)..
Both the ERJ and Airbus A318 have specific steep approach modes which are activated by push buttons. In the Bus it's located on the overhead and in the ERJ it's located on the glareshield left of the MCP.
When activated on the Airbus, some of the spoiler panels come up 30 degrees and the aircraft needs to be in full landing config. The EGPWS system will change its logic to allow for the approach. Additionally, the ECAM will add "STEEP" in green to the landing config page. The pilots will also get extra callouts, one of which is, "FLARE." That occurs somewhere around 63 feet. I don't remember what the other callouts are.
I don't know as much about what happens with the ERJ except for the fact that the EGPWS system logic also changes to allow for the steep approach.
I believe there's a video out there on YouTube of an ERJ doing a steep approach into LCY, but I can't look for it right now.
Hope that helps. (At least with those two planes).
EDIT: Just found this presentation on the specifics of the Steep Approach mode in the A318. http://www.smartcockpit.com/data/pdfs/plane/airbus/A320/misc/A318_Steep_Approach_Operations.pdf