We brought our at least 10 yr old fridge (hand-me-down from SIL) - the bloody thing survived too, was hoping for an insurance claim, but it's chugging away resignedly in rather more heat that it was used to!
Apart from that, we had sole use of a container and I brought everything conceivable - down to Lidl moisturisers, deodorants, big Tresemme shampoos, huge boxes of washing powder from Costco (Persil whites and colours) and Comfort. Blocks of plugs from Poundland (3 sockets in one board) so we could (pay to) change just one plug (good old WA), plus UK to Aus adapters bought off ebay - we brought those in hand luggage so we could use stuff like hairdryers, radio etc while we waited for the container to arrive.
I also bought a Squeezebox digital radio, which I found an app for so I can listen again to all BBC radio from up to a week ago, so can listen to the night time show at the right time, if you see what I mean.
Umm, new hoover, just a crappy one from Asda, but it does the trick in a largely hard-floored house, plus a floor mop with a couple of replacement heads. Hot water bottles, heated throw, 1 tog duvets from M&S. We needed to buy new mattresses anyway, but UK king size fitted sheets fit an Aus double, flat sheets fit Aus Queen (their King equivalent) fine. Pillows from M&S.
I have had HUGE use out of this Heated Airer as it's not always warm and sunny, even in Perth
, I had one of these sent out by my mum as we're in rented and it saves cleaning the oven : Lakeland Oven Liner
Anything you can stock up on, if only for convenience value rather than cost, as although you can find decent-ish prices on stuff if you shop around, sometimes you can't be bothered, and it's unimaginably comforting to crack open a Soap and Glory body butter or something (well it was for me, a sad person!) Paracetamol is amazingly expensive compared to supermarket unbranded stuff, as is antihistamine tablets - slap an order in with Chemist Direct or the like and stock up.
Right, last few things - I brought 2 huge bags of Yorkshire tea bags from Costco, again, very comforting.. There'll be loads more things but I'll embarrass myself further showing what an obsessive packer I was!
PM me if you'd like any other info. Good luck!