slip and turn,
LHR and LCY were using the same set up again this morning. It is probably the most common in daily use. Without the plates in front of me just now I am guessing, but that bit of sky just north of Canary Wharf where conflicts could occur in the overlapping STAR and SID might be as small as a cube with 2000 foot sides but usually when there's a LCY SID and LHR arrival converging, you see the Heathrow traffic either turned early nearer Tower Bridge or extended a bit downwind almost to overhead LCY 10 Threshold whilst the LCY traffic is obviously directed to keep its head down in the climb.
When the sky is free of LHR traffic, many of those RJs skyrocket out of City and in one sweeping turn exit to the north and/or then round to the east quite literally like bats out of hell. They often remind me of the Lightnings and Canberras skimming the horizons of my childhood!
I don't wish to be rude but much of what you write here just indicates you don't really know what you're talking about.
LCY and LHR operate autonomously of each other. Simply put LHR arrivals descend to 4,000ft and cannot go below that until a set point that is clear of the LCY SID track. LCY departures climb to 3,000ft and cannot go above that until outside of the lateral boundary of the LHR RMA.
There's no interaction between the two units at all bar unusual circumstances i.e. LHR don't alter their vectoring if there's a LCY departure or not. The only thing that dictates where the LHR base leg is is how busy it is and how many are off the stacks on intermediate approach, there's a natural ebb and flow in and out and I stress again it's nothing to do with what LCY are up to.
Obviously if either an LHR arrival or LCY departure busts its level in the area you're talking about there's potential for an incident, but the same is true in many other parts of the TMA. This little corner of it is in no way unique.