We have a huge 30m+ garden (ex council house when land was dead cheap) and the clay soil is terrible, also loads of bricks and rubble buried in it. To be honest I found it's best just to accept it and avoid the garden at all costs for 6 months of the year. It looks awful in winter and loads of standing water after heavy rain, but it normally sorts itself out. Militant aerating and removing all the moss didn't have any effect whatsoever, and anything else would be too labour intensive and way too expensive. Strangely enough it often needs watering in summer!Make peace with it!