between the time the stricken aircraft took off and it declared an emergency how many planes had already departed 27L?
None.
There was only one departure in the hour after BAW762 took off at 08:17, and that was from 27R at 08:38 (BAW165 to TLV). The first 27L departure after that was BAW758 to Bergen at 09:23.
You can see them on WebTrak although, as a previous poster has mentioned, for some peculiar reason all Friday's flight have been anonymised.