I agree re the clothes - I may have already mentioned it upthread but it is seriously more expensive here, especially for children's clothes, and the "cheap" end quality isn't even as good as, say, Tesco
Baby popper vests, for e.g. - pack of 2 from the cheapest place here was $8 (currently standing at ~£5) - I could get at least 5 for £5 in Tesco.
Although we didn't bring any big white goods, we did bring the kettle, iron and toaster, and several multi-socket plug extension leads. This saves on having to change the plugs over here; and means I only have to have a couple of UK-->Australia adapters, which are pretty expensive and not always easily available - it's almost worth getting travel adapters in the airport rather than buying them here.
We also brought our DVD player. Because Australia is Region 4 and the UK is region 2, many DVDs won't play on an Aussie DVD player (and Aussie ones won't play on our UK DVD player either). We have both plugged in, and just have to remember which place we bought which DVD from. Although there are ways of "cracking" the DVDs, someone who has tried this (and I don't know which brand with) says her DVD player only switched regions 4 times and then got stuck on the last one - so frankly, having 2 DVD players is a lot easier.
Another point to make is that over here, bargaining with the retailers of homewares, especially electrical goods, is normal and expected. If, as we were, you are buying several items at once, you can really drive the prices down and get a good deal. So far, we have found Good Guys to be the best for this - DH nearly made the salesman cry because he took him down to the limit and then asked for a free DVD player to be thrown in!! He got it for $10, I think. But they also all do competitive pricing - so if you find a better deal in another shop, you can make them match it. DH did this with Harvey Norman for our TV.
It doesn't really work with any other type of shop though...
TBH, if the company is paying for your shipping, you might just as well bring as much as you can. You can always junk it when you get here if you decide not to keep it, but you might find it hard/expensive to replace so it's worth having it here in the first instance. When I went back to the UK the first time after moving out here, I sent another shipment by sea of all the heavy small stuff that had got missed from the first pack, or that we had needed in the UK and couldn't allow to go - it cost me another £140 but it was well worth it! And still cheaper than re-buying it all here.