I just booked flights from MEL to Manchester (& back), and the booking agent recommended either Emirates, Singapore, QANTAS or BA.
The prices were similar for all of them (some sort of special offer on over here last weekend), a total of AUS$ 2100 ish each (that was for travel in April) which I think is about 750 to 800 quid at the current (terrible) exchange rate.
I think the prices were the same to LHR, but that may just have been because of the special offers).
We booked with Emirates, because we'd both heard they were brilliant from a variety of people (including the agent), and they weren't the most expensive.
I flew out to Oz (one way) with JAL (cheapest when I booked), and would not recommend them, the seats seemed more cramped than I was used to (I'd only done European flights before that). My girlfriend flew over with Singapore and was well impressed with the level of comfort and equipment (screens in seat backs etc, JAL only had one projection screen at the front of each section, and cr@appy films to boot).
Most opinions I've heard put Emirates or Singapore first, then QANTAS and BA, but I've never met anyone who's tried all of them!
You might also try asking in the Pax & SLF forum as well as the Dunnunda forum.
I came out here for a year about 3 years ago now, and am only going back to the UK for a holiday!
Edited to say all flights were cattle class.