Obviously it depends where you are moving to :)
I found that living in the USA, that what I wanted from the UK diminished year on year. On visits, I used to stock up on children's pyjamas for some reason - the US ones are just nasty.
We could get British food where we lived - well the kind that is dried, concentrated, tinned. Of that, I'd buy orange squash, Ribena, Marmite, Heinz baked beans, Heinz soups (when I was pregnant), tea. The food I missed was the kind I couldn't get there anyway - sausages, bacon, cream cakes, etc - but it wasn't a big deal to go without.
In the US, you can find most things anywhere (unless you are seriously in the sticks). Some people think that if it is not in Walmart or Target (such as a decent electric kettle), they don't exist, but there are plenty of specialist shops in the normal shopping malls and plazas.
Cheap French plonk was something I missed when I first arrived in the US - I really resented spending $8 on a bottle of Glen Ellen gut rot. I was very pleased to find Cotes de Gascogne at £5 a bottle in our local, extremely posh, wine shop (where most wines were in the $25 - 50 range) - I think he bought it in specially for me.
Baby stuff may be something that you are particular about. I could never find a decent buggy in the US - they all were made for people who were no taller than 5'1", so I did have a Maclaren sent over from the UK. Later on, these did appear in the US shops.