You can apply ferrous sulphate to control the moss but all you will be doing is controlling it, not killing it. It will return if there is an underlying problem but you say you have good drainage and have been aerating and scarifying. In that case there are a number of other possible reasons

1)Too much shade
2)You are cutting the grass too short, weakening the grass and allowing moss to get a hold
3)The grass plants are not dense enough
4)The soil is not very fertile and so the grass is weak
5)The soil is overly acidic - moss prefers acidic soil

I would encourage you to raise the height of your mower, overseed the lawn after scarifying to make the sward more dense and make sure the soil is as fertile as possible to encourage the grass to out compete the moss. Mulch mowing will help return nutrients and organic matter to the soil which is very important when growing in sandy conditions (sandy soil loses both very rapidly). Not only will nutrients be returned but the organic matter will help with water and nutrient retention, again ensuring your grass is as healthy as can be.

If you can get your soil tested and it is overly acidic then applications of lime may also help with the moss and help unlock nutrients which are unavailable to the grass at present.

Hope that helps, Stuart.