Build up soil for lawn

cprice2701Da2ylRd3

I moved into a new build last year and I'm almost ready to get the lawn sorted. I've dug out several tonnes of heavy clay behind the retaining wall that we built in order to get a level lawn area. I now need to backfill but I'm not sure what kind of soil to buy. In some areas its well over a foot deep so just filling it with topsoil would be far too expensive. Will I be okay backfilling it with a regular subsoil or will that cause a drainage issue being sat on top of more clay? If so, would I be better off mixing a good amount of compost into the subsoil?