Hi, We have been here for three years now and have been through all of this, we started off renting our primary residence back in the UK and the bought after a year of being here. A few things to note :-
Any rental income in the UK should be declared here, many people don't but the ATO are not the inland revenue they probably will catch you at some point !
If you previously had any rental properties etc in the UK and had any carried forward tax losses these will be lost in Australia as they do not accept them even if they were clearly shown in a UK tax return, the ATO is only interested in your tax affairs from the day you arrive as a permanent resident in Australia.
In the UK your main residence will not be liable for any CGT for three years and after 5 the UK disregard it and treat you as non resident however Australia technically value the property from the day you become resident.
When you buy a property here that starts the CGT clock on your UK property, if you held any buy to lets etc they would have started to be liable to Aussie CGT from day one.
If you did or do have any buy to lets if the property falls in value (as was our case unfortunately) from when you become resident to when you sell you can also then claim a CGT loss on your Australian return which you can then use to offset any future gains here.
One final thing when doing any transfers of money etc don't use the banks use a currency broker like HIFX or similar as they have much better rates and dealing with them is pretty straight forward.
Hope this helps.