Interestingly, few of the ATCO's I know "risk" flying the Lea Valley - preferring the Dartford option! As you say - it is negligable in terms of time (but less picturesque for the pax!)
I am not saying that LCY wouldn't accept you if in dire straits - but landing on an unfamiliar aircraft carrier with a narrow runway in an emergency needs a cool head. I think I would end up swimming!!!! I would far prefer a sports pitch! Any LCY based aircraft generally divert elsewhere in emergencies (normally STN).