Garden like a building site

[hmallett]

This week I did the first cut of the lawns. We moved in to this house in October last year, so  only mowed lawns and weeded them at the end of last year.
The back lawn is in poor condition. There are patches where weeds have grown, and the grass is very thin. Upon investigating these points, (by trying to aerate them) it turns out that about 75% of the lawn has lots of stone within 4" of the surface. In some places it appears there's only about 1" of soil before you hit stone. The only area that's not too stony is slightly sunken, by about 3". One stone which was poking through the surface turned out to be about 12" x 8" x 8", which left quite a hole in the lawn! By stony I mean there's no way to get a fork in any further.
The soil is clay, and only about half the back lawn gets direct sunlight. The house was built 8 years ago, and it seems we still have half the building site under our lawn.
Given that the lawn is so poor, and the ground full of stones (and maybe more large rocks), might the easiest thing be to sacrifice what we have, dig over and remove stones, then seed the grass from scratch? I'd rather invest some time and effort and have a decent lawn, than be left with our current mud and moss mix.

[Grassman]

Given that the lawn is so poor, and the ground full of stones (and maybe more large rocks), might the easiest thing be to sacrifice what we have, dig over and remove stones, then seed the grass from scratch? I'd rather invest some time and effort and have a decent lawn, than be left with our current mud and moss mix.

Not the easiest no. The easiest would be to import enough topsoil to give you at least a 4" covering into which a new lawn can be sown as from scratch, but that may not be practical option given the increase in height or the cheapest.
If you are restricted by the heights and levels of your lawn area then digging over is certainly the way forward, although don't forget that if you are removing material from the site (as in stones, rocks or builders rubble) you will almost certainly need to replace this with the equivalent amount of topsoil or you will end up with a sunken garden.
If you have access, I would also consider the use of a mechanical mini digger as these machines are reasonably cheap to hire and are capable of saving on an incredible amount of back breaking work. The smallest machines fit easily through a standard garden gate.
However you choose to complete this task remember to get good soil consolidation before sowing.
All the best