Have you had the soil tested for pH and other elements such as phosphate and potassium? We've just had ours done - will get the results next week. The pH test was free - a more comprehensive one was £25.
If the soil has a low pH - below 6.5, then grass doesn't grow as well as it could, so you can apply lime to raise the pH. One tonne to the acre raises pH by 0.3 points, I think.
Our Sheepfold has old grass and other plants, but moss as well. This year, I'll have lime applied if it needs it and it will be harrowed to take out the thatch and let the air in, encouraging the gras to grow. If it needs anything else, I'll take advice from the chap that did the testing. I have told him that I don't want to apply nitrogen as it doesn't fit with how we want to do things here. The hardest bit is getting a contractor to spread lime because we're so small.