We have built our house on a very clay soil. We have scraped a lot of the clay away but we still have clay to work with. The clay is holding water even with the land drains we have installed. Can you suggest what we need to do to grow a lawn onto the clay

To improve your clay soil will be hard work. You've taken the first step - now you need to dig it over ASAP and let the frost get at it - this breaks down the clods. Then, in the early spring, dig in loads of organic material - as much as you can get hold of, including some manure. Also dig in horticultural grit. All this really will help the drainage. Then prepare the area for turf laying - I think this would be better than seeding as you will be adding another layer of good soil. The ground has to be raked and all weeds and stones removed, then raked again before you lay the turves like bricks - off-set and filled in at the end of the row. Water well.

I know that this is hard work, but your new lawn will be much better for it. I do wish you luck and success with it.