Beside the pax issue, it's generally hard to estimate without the exact weather parameters and aircraft type. Fuel burn does roughly depend on air speed, but not to the speed over ground. Therefore you need to calculate the time you need and then multiply this with the average fuel burn per hour. And even this only gives you a rough impression:
If you do SYD
(tail winds) with an average speed of 475kts / ~920km/h you roughly need 20:40h (plus the time on the ground, although you don't consume fuel there.
Lets assume you can do SYD
(head winds) nonstop, which even the 772LR won't be able to do (unles the weather is extremely advantageous) and you reach an average speed of 430kts / ~800km/h you will need 21:16.
could be better, but the judgement could turn into the opposite in case the weather is different in a way that speeds are different. But certainly the SYD
leg doesn't get better if have to do a fuel stop at lets say HKG
as it certainly increases the total amount of fuel needed.
Edit: The time needed is almost equal on both routes in case you only fly at an average speed of 465kts / ~900km/h on SYD-ANC-LHR. The pax issue is not enough reason either to choose the westbound route. Maybe offering a LHR-ANC flight gives you enough pax to fill the bus, LHR-HGK is served by many others.
[Edited 2005-05-23 16:32:42]