EU passport holders need eVistor - link is via official website. make sure you have 6 months validity at least (from return date) on your passports though, def need for Singapore although can't remember for Oz.
I've been to Australia twice in the past month and have never paid for my visa. If you're a British passport holder, it should be free and lasts for a year from when you first enter. Never had any problems and it takes about 2 hours or so to be processed and come through.