a quick search came up with Macquarie Bank in Australia. I do know a little about them as I was looking for a broker when I lived in Australia. It is an investment bank with offices in 28 countries around the globe.
they do broking as well, Australian stock, cfd~s and futures are on the menu and they are a member of CME, Liffe etc.
as far as I know, you can open a bank account in your name at one of the big banks of your choice and you authorize them to withdraw funds for your purchases and they will deposit into your bank account when you sell.
you can open accounts on the internet.
I will look into this in detail myself and if I`m happy with the results I dont think you can get it any safer.
ps: thanks Jack for your research