If, by bricks, you mean whole, unbroken house bricks, you could, fairly easily, do a paver type drive. If you need more bricks they are probably one of the least expensive paver blocks one can buy, at least here in the U.S.
The clay could be excavated by only 3 or 4 inches and then backfilled with a good quality sand. This, too, is inexpensive. Once the sand is in place it should be compacted with a motorized compactor (rented from your local DIY supply). Extra sand should be on hand to level any low spots. The bricks are then just layed in whatever pattern you choose. Additional sand is scattered on the finished drive and had swept over the surface to lock the pavers in place.
There's special plastic edging that's "L" shaped to hold the edges. Very nice looking and durable...