We are HEAVY clay here too. We layed a turf lawn on 2 tonnes of topsoil mixed with sand. It still cracks in dry weather and floods in wet weather!
You shouldn't walk on it to begin with, but we, I think, were too precious about ours and it has suffered for not being trampled/camped/picniced on!
Make sure you remove any weed roots etc. as we did, however some of the little buggers have found their way up through about 8 inches of beautiful topsoil!