If i buy an unlocked phone in the UK will it work with in Australia?

What model phone it is? Almost most of the unlocked UK phones will work in Australia. But it depends upon what method of unlocking have been followed for the phone. Most of the flashing methods or Software unlocking may damage the phone's hardware or software. So it is better to unlock it using unlock code. Unlocking a mobile using unlock code won't affect a mobile phone's performance in anyway. So be wise in choosing a reliable source to get the unlock code for your mobile. For example you can get the unlock code from http://www.Superunlockcodes.com/ this site provides accurate unlock codes at affordable cost. Once you get the unlock code you can visit http://www.Mobileunlockguide.com/ this site provides free unlocking instruction guide which would help you unlock easily.

as long as it is modern phone and it wasn't stolen in Australia before [will get blocked if was stolen and registered such]

if it operates in the same frequencies as the cell towers in australia..