LHR to DXB = 6 h 45 m (Source: BA)
DXB to SIN = 7 h 00 m (Source: Singapore Airlines)
SIN to PER = 5h 00 m (Source: Singapore Airlines)
PER to CHC: Air New Zealand don't seem to have any direct flights. They quote 8 h 55 m as their shortest journey time, changing at Auckland. Qantas don't seem to have any direct flights. They quote 10 h 05 m, changing at Sydney.
CHC to NAN = 5 h 45 m (Source: Air New Zealand)
NAN to LAX = 10 h 50 m (Source: Air New Zealand)
LAX to LHR = 10 h 30 m (Source: Virgin Atlantic)
Chris