When are you travelling? There are quite a few good fares to MEL from London at the moment, CX(Cathay pacific) and QF(Qantas) are both around 650.00GBP on certain dates and will certainly be a lot quicker than going via the US.
Late last year I went to Sydney with BA(British Airways) and CX with a couple of days in Hong Kong both ways for around 750.00GBP. Something like that might help break up the journey a bit unless you want to just get there as soon as possible. If that is the case Qantas are worth a look, options via Dubai, Singapore and Perth on the new service starting late March.
Spike