From the BAA website, just to give a flavour of the number of flights scheduled in before 0600 today.
04.45 BA016 SYDNEY VIA SINGAPORE LANDED 0439 4
04.50 BA026 HONG KONG LANDED 0433 1
04.50 VS201 SYDNEY VIA HONG KONG LANDED 0436 3
05.00 BA032 HONG KONG LANDED 0454 1
05.05 BA064 NAIROBI LANDED 0519 4
05.05 BA074 LAGOS LANDED 0624 4
05.05 CX251 HONG KONG LANDED 0457 3
05.15 BA056 JOHANNESBURG LANDED 0505 1
05.25 QF009 MELBOURNE VIA SINGAPORE LANDED 0534 4
05.30 MH002 KUALA LUMPUR LANDED 0549 3
05.30 SQ322 SINGAPORE LANDED 0514 3
05.30 BA010 SYDNEY VIA BANGKOK LANDED 0516 4
05.30 BA212 BOSTON LANDED 0444 4
05.45 KQ102 NAIROBI LANDED 0613 4
05.50 BA058 CAPE TOWN LANDED 0618 4
05.55 UA958 DENVER VIA CHICAGO LANDED 0543 3
05.55 BA018 MELBOURNE VIA SINGAPORE LANDED 0540 4
PS I have removed the code sharing flights and just left the operating airlines flights.