I am planning a trip to Australia:
This will involve staying with relatives in Adelaide, but also I intend to include visits to Cairns, Alice Springs, Melbourne and Sydney.

Is there some sort of "value" ticket I can purchase which allows me a certain number of internal flights within the country;
or is it a question of what I can negotiate when I make my initial booking from the UK?

I am an aussie, and have done a few internal flights within Australia with some of the cheap budget flight companies such as jet star and virgin blue. I'm pretty sure they dont have the option to do several trips on the one ticket, so you would have to buy individual tickets. These companies are cheap, so just look out for their sale fares and you will get some bargains.

Cheers,
aussie23