ttodd
In your situation, even if I was flush enough to afford the long taxi ride to LHR or LGW, I'd still definitely fly from LCY, instead of dragging myself and my baggage across London on hot and crowded trains. I've found that the DLR & Tube from LCY, even only to Bank, is a bad enough hassle, up and down steps and escalators, plus never-ending tube station walkways.
Direct from LCY, you'll start your air journey in a much more relaxed state of mind. Bon voyage!