slip and turn,
I'm glad you've enjoyed a few hot dinners watching the traffic out of the window, I've enjoyed twenty odd years watching the same bit of sky from a radar display
Hopefully one of my colleagues will come along and back me up, but I assure you LHR traffic and LCY traffic is primarily separated vertically, not laterally, in that area. To do the former would simply not be practical. The respective controllers do sit only a matter of feet apart in the same ops room but can go a whole shift without having to speak to each other operationally, the procedures are set up such that in all configurations the two airports operate independently of each other (well when LHR are on the 27s and LCY on 10, though still independent ops the LHR folk take a close interest in how far downwind the Thames folk take their traffic, but that's another story).
If you see LCY departures doing slightly different things it's either because they're not following the SID track exactly or Thames, for their own reasons, have taken it off the SID early... but that is 99.9% certainly nothing to do with LHR traffic.
Below is an fairly old plot of inbound tracks to LHR, where you see the plots of traffic joining final approach at different ranges that's nothing to do with avoiding LCY traffic. It's just the natural way that the final moves in and out depending on the volume of traffic.
