I REALLY wanted to do this, largely because the flat pack stuff like Pax at Ikea is rather terrible and not all that good in price and I prefer older nicer wood and styles but most of what you can buy is horribly proportioned. IE I was Pax wardrobe size, but made of proper wood, with proper joins and looking like proper woodwork.
Unfortunately after some reading and a little playing around with wood, you really need a whole range of tools to make something not entirely crap, and you need to buy wood, be able to store it somewhere for a while, perfectly flat, to dry out, and the time/space to build it.
Thing is, you can make a very basic Pax type thing out of chipboard/plywood pretty easily I'd think, but it wouldn't be great quality, you could do it with minimal tools though. A half decent wardrobe and, meh, its not something you can really dabble in or just have a go at. I've always wanted to get into woodwork and build things, but its so hard to start from scratch without a family member/friend who has the tools/skills, to help you through.
Though maybe something like a woodworking class might be something you could look into, I couldn't find one, or afford one, or get to one easily so I've all but given up on the idea of making anything beyond small boxes and fixing a few drawers around the house.
Doing something fairly basic though, if you really don't care if it looks too bad, can be done pretty cheaply. You pretty much just want to build a basic frame, which isn't much more than a elongated cub, with the wood screwed and secured into the wall in the recess, then buy some kind of cheaper wood to make two doors out of and sides(if they need to be deeper than the recess), a couple packs of hinges for £10, some cheap handles and some paint.