Sorry ladies I was offline for a couple of days! It is indeed the Expedit 8 cube (2 cubes on the left are hiding in the pic) from Ikea.
Then you can buy Expedit drawers, or even a door that are made to fit inside the cubes and they screw in to be completely safe.
We got the gloss white cabinet which was a touch more expensive at $150 ( think non gloss was $100) plus the drawers were $30 each. So worth it !
So in the bottom I'll probably use baskets - I didn't want to use them up too and risk bub pulling them on herself