This is my pet method for subframe construction.
I like to use a laminated frame as this makes it more stable and also allows you to fabricate half-lap joints rather than the much weaker mitres.
You need some wide but thin timber. The easiest to get and cheapest I've found is pine tongue&groove cladding. You need to square off the tongue side, but the groove side is no problem.
It's easy to build. First cut four pieces the same size as the outer dimensions of the mirror. Lay them out and put a screw though each corner. Square it up by measuring diagonally. When all is true, add more screws to keep it so. Next, unscrew each corner in turn so as not to disturb the squareness and glue it well and add as many screws as necessary. You can also add cross-braces if need be.
After you do this simply fill in the gaps to form the full thickness all round.
At this stage you can make a sneaky hanging point by cutting down the width of one of the fill-in pieces on the top rail. This forms a little cavity that will fit over a complimentary batten fixed securely to the wall.
Then you just need this:
http://www.screwfix.com/p/geocel-trade- ... 10ml/95057
This will form a very secure support for the mirror. You could hang it on the wall without the outer frame which is virtually relegated to just tidying the edge. The subframe will probably protrude fro the back. This makes attaching it to the subframe easy. A few LION bendy plates will do the trick.
The best thickness of cladding to use is maybe 8mm. Which doubles-up to 16mm. add 6mm for the mirror and you have 22mm to swallow. Depending on the profile of the frame you could paint the edge of the subframe black or add pieces to the back of the frame.
I wouldn't rely on the frame to support it, no matter how you try to beef up the corners.