Use a fork or aerator to make 8 inch (20cm) deep holes about half inch (1.5cm) in diameter all over. Then fill them all with B@Q/Wickes sharp sand (lawn sand costs more). May need some repeating over the next few seasons. Feed (cheapest high nitrogen) and cut with the blade set higher to give the grass a chance to grow.
Also ensure the site itself is draining as it may not be just a soil problem but general drainage.
As an aside, I tried this once in my front garden and cut through my telephone/TV cable as the cable company puts the optic cables so near the surface with almost no protection. Now I live with the moss.

Thanks for the reply, will give it a go and keep you posted .olly :)