Horrible stoney grass

[JorisBonson]

We moved in to our house last summer and didn't tackle the garden at the time. Now we have to 😕

I have a 30ft garden, very patchy grass with clay - ey soil. There's stones and crap everywhere, made worse by the new fence we has installed post storm Ciara.

I tried to plant things last year but the grass / dirt is so shallow (I am not a gardener by any means so don't know how else to describe it!) that everything died, despite my best efforts.

How can I have half decent looking grass on such short terrain?

Does the garden have access for a digger? I'm normally one for trying to DIY as much as possible, but it sounds like the top layer of earth needs excavating and taking away and new topsoil adding. Realistically you need arounnd 4 inches of decentish soil for a lawn to establish and have some resilience to drought.