You can get almost everything at Bumps to Babes in Ap Lei Chau or at their Peddar St. branch. They sell the UK Pampers which are definitely better than the version sold in Wellcome etc., just more expensive. They can usually order anything that they so not have in stock, but then you have to pay shipping. You can buy Sudocrem, anti-bacterial wipes, Carex soaps etc. there that I have not found elsewhere here.
There is no Gap here, even though you can buy lots of BabyGap stuff in Stanley Market (a whole lot cheaper), the range tends to be a season out and more limited. Same applied to Next. I load up on Gap socks when I'm in London. I also like to buy a few co-ordinating outfits, which they tend not to have in Stanley. There are plenty of wonderful children's stores though, and the shopping centres are very well organised so that most child-related shops are located on the same floor as one another. Singapore has even more , so you will not have to fly all the way home everytime that you need to stock up.
You will find Start-rite shoes here, but I have only found one store that stocks them and they have a much more limited range (and cost about twice the price), so that's another thing on my list every time that we return. Children's shoe stores in London seem to offer a much more extensive range and better fitting service. Unfortunately you cannot really place an order with grandparents or other visitors when they fly over as the child obviously needs to be present for the fitting.
I would bring lots of BBC DVDs of your children's favourite programmes though, as Playhouse Disney and Nick are not as good from an educational point of view for young children.
I'd still bring your whole nursery, buggy etc., as the marginal cost of shipping is minimal. Even in the year that we've been here I've noticed a lot more stuff available.
The one thing that I still miss is organic and 'homemade' baby and children's meals (I used to buy lots at Cook and Waitrose). I guess that because most people have helpers, they do not have the demand here. Miss foodhalls too. I cannot believe that I am admitting this, but I even miss M&S ready meals (although I was never a huge fan when I could walk down the road to get them. Cannot ship them though.
Will post if I think of anything else. Good luck with the move.