I have been caught out by this too. Simply stops me flying from LCY. BA have little sympathy with people missing flights or at LHR, conformance - I know from personal experience. With a 135 minute train ride with 1 connection into Kings Cross followed by the underground transfer to Bank and DLR to LCY, the risk averse nature in me would never allow me to plan to arrive 2 hours before departure.
As far as I can see, at LCY BA operate as London airways for London passengers. It is not an airport for the masses.from the regions.
I will now put an thick Beano down my trousers - shoot away.