I'd build an MDF carcass around a bisciut-jointed wooden frame. (Or at least around two frames of 2 x 2, (50mm square). One at the top and one at the base. Don't forget to plan for a kicking strip at the base.)
You could use a Domino to joint the frames but that depends on the depth of your pocket!
See if you can find Paul Levine's DVD (FWW Taunton) on building cabinets and you'll get some great ideas.