In Scotland my soil was clay and was always waterlogged after rain, i solved it by digging a couple of holes about 7 inches wide, i went as deep as possible by hammering a steel pipe into soil, taking it out and removing the clay kept doing this till i had a decent depth in my case about 4 feet, then filled the holes with pebbles to about 6 inches from top then added soil, it worked a treat, never had water on lawn again, good luck.