Ok I have never had an issues solving a problem, by booking my flights from Singapore.
I have just searched for you.
Darwin to Singapore return just over $300 (in 3 months time) Dethstar
Pre booked on the net is-
Singapore to London return $1205 (Qantas)
That's just over $1500.
Tried on Qantas web page by coincidence, it also goes via Singapore.
Return is $3600 for same dates.
So it really is cheaper and same airline except Darwin Singapore! Oh dam that's actually operated by JETSTAR.
Same thing $2,100 cheaper.