just doing this myself at the moment. From what i have read from the turf manufatcturers web sites now is a good time to lay turf. For seed its too late though.
I also have clayey soil. Unless it is raining or has just rained then the rotivator will just skip along the top of the baked clay and wont do a thing to turn over the earth. A pick axe is all that will work.
You then need about 2 inches of decent soil for the grass to sit on. This may mean diging out 2 inches of clay if you want to keep the same level, or just put it on top of the clay.
The main problem i have had is flattening out the area. My lawn is so up and down i was moving barrows of earth and digging up all day. back breaking work.
Good luck.