Web Master:
Firstly, was the sand/soil mix spread across the whole lawn or only where the grass has now died? If you did cover the lawn with the sand/soil mix it seems unlikely that this is the problem as some parts of the lawn seem very healthy.
The bare areas look quite compacted so the rain may be running over rather than into the soil. Make a hole in the soil big enough to see how far the rain is permeating, after all the rain we have been having I would expect the soil to be quite moist to a reasonable depth. If the soil is still quite dry i would try things that would help the water permeate the soil. Firstly, by aerating the soil with a garden fork and secondly using a wetting agent to reduce the hydrophobic nature of the soil. Once the soil is moist it is a good idea to fertilize the lawn.
This has been a long hot summer and so many plants have not survived, you may need to sow seed or have the dead areas replace with turf. Because it is quite a large area I would recommend speaking to a lawn specialist before re-turfing the area.