You can veneer heavy duty aluminum foil to MDF using spray adhesive. Buy the heaviest foil you can find, and spray both the foil and the substrate with the adhesive. Let the glue get tacky, then carefully affix the foil to the MDF. You'll only get one shot at this!

For a brushed-aluminum finish, lightly hand sand with 220 grit paper in circular motions. You'll need to protect the fragile aluminum with some type of finish coat like polyacrylic, or polyurathane.

I've built a number of clocks using this technique (including a floor clock that was 5 feet tall) and they turned out great.

Good luck!