The drawers were quite shallow IKEA drawers. We turned both drawers sideways and then screwed down a top to make them into a desk. Coat of paint and ....ta dah!
Must get a desk chair and so on but the little one is pretty impressed with it so far.
While we were at it, we did another of the children's drawers that also had *ahem* similar issues.
Looks heaps better now.