We had a similar problem in a two and a bit acre paddock. We had spoken with a grassland advisor when we saw his stall at the Highland show - probably wouldn't bother with such small fry as us if there'd been any of the big boys asking questions
He came up with a species rich seed mix, suitable for our primitive sheep (which don't need really rich grazing) which was heavy on white clover and had a variety of better grasses in it. This we sprinkled by hand in spring - just took a few hours with two of us. Thinking back, I think we raked it with a tractor towed rake first, which removed the thatch and created some bald bits, plus opened up some scratch marks the seed could fall into. you could use a disc harrow too. We did it just before it rained, so the seed could be washed into the bare bits, then rolled it.
For the first year we couldn't see any improvement, but the following year other grasses sprang up and plenty of clover. Because of the carefully chosen seed mix, our wildflowers still come back, and we have even had orchids.