Peter,
Take your normal mowing or grazing right up to August, then second or third week in August best time to break it up and sow seeds, if they get away promptly with some rain there will be some light grazing in the backend, and will get a full cropping year the next spring.
I always think that the young seeds are best rested through the winter, and as the soil dries out in the first spring, the roots are strong enough to follow the moisture down, giving a more reliable crop.
Trouble with spring sown seeds is when you get a very dry May, and you struggle to get much production that year. The grass roots are not mature enough to reach down to the moisture.