How can I improve the draining in my garden?

My house is built on an old school playground and drainage is very poor with lots of moss and wet areas. There's a thin layer of about 3-4" topsoil, then a mix of rubble and poor soil about 6-9" deep, then tarmac, below the tarmac the soil is sandy and very compacted. I've dug some drainage holes up to 6' deep which has helped a bit, but is there a better way of improving the drainage, maybe something I could plant that would send roots down to break up the lower layers or just feed off the water. It's not a huge garden so something big like a willow tree wouldn't fit.