They are all tough periods outbound due to the summer season. For years I have successfully travelled to Europe via Japan. Out of Narita there are 5 departures within 5 hours (Virgin, Japan Airlines, Air Nippon and BA) - all 744's and 345, all with plenty of capacity. This might be a longer journey then via SIN/BKK etc, but you always get to LON without issues, and on occasion, BA has upgraded staff ex NRT to LON in WTP.
SIN/BKK are the premium routes for QF/BA so they are always the toughest. I would rate HKG to LON as number 1 if you are choosing to go via this region. The only bonus ex SIN is you can go to FRA/CDG/HKG/LON on QF/BA/AF/CX to get to LHR, but you are also competing with a great deal more staff and commercials (and our favourite - freight).