Ok, so from a quick google and FOI request results, here's the full list of all post boxes at Heathrow Airport, with post codes. However the exact locations aren't there, so it's not terrible helpful.
Originally Posted by Royal Mail
TW61EY POST OFFICE, TERMINAL 2
TW61SY VISCOUNT WAY, HATTON CROSS
TW61AP DEPARTURES, TERMINAL 1
TW61AP ARRIVALS, TERMINAL 1
TW63EQ POST OFFICE, HEATHROW CARGO
TW61AP DEPARTURES, TERMINAL 1
TW61XA ARRIVALS, TERMINAL 4
TW61XA ARRIVALS, TERMINAL 4
TW63XF AIRSIDE, TERMINAL 1
TW61PN ARRIVALS, TERMINAL 3
TW61PN DEPARTURES, TERMINAL 3
TW61PN DEPARTURES, TERMINAL 3
TW63XF AIRSIDE, TERMINAL 1
TW61XA DEPARTURES, TERMINAL 4
TW61XA DEPARTURES, TERMINAL 4
TW62SW ESHER CRESCENT
TW61BU QUEENS BUILDING
TW61BW AIRSIDE, TERMINAL 2
TW61PN AIRSIDE, TERMINAL 3
TW61XA AIRSIDE, TERMINAL 4
TW62NR TERMINAL 5 AIRSIDE
TW62NR TERMINAL 5 DEPARTURES
TW62NR TERMINAL 5 DEPARTURES