There are a few things I would recommend doing to any website regardless of TLD to show geographic relevance.
1. Host your site in Australia. If you are in the UK and have a .com then at least make sure the site is registered with an Australian registrar and hosted on a server in Australia. That should be the first thing to do.
2. Be sure to put your Australian address and contact information on the site. Probably more than just the contact page...put that type of info in the footer so it is sitewide and Google definitely spots it.
3. Buy your .au domain name and 301 redirect it to your .com. I would even buy other .au domain names and redirect them to your .com. Be sure not to buy hundreds of existing sites and redirec them though, as this is creating doorway pages and is considered black hat SEO.
4. Focus all of your link building efforts on .au domain names. Make sure you are in Australian specific directories as well. If you have a location with a physical address, be sure to get into the local directories too.
5. In Google Webmaster Tools under settings you can specify your country and language I believe. Make sure you tell Google you are targeting users in Australia.
If you follow those 5 steps you should definitely increase your relevance in Google's mind to the Australian audience. Good luck!