Sad Lawn Advice

Hi all,

My back garden is in a rather sorry state. A combination of poor sun, poor drainage (3’ of compacted soil on top of concrete slabs) and even worse lawn care (by myself and my furry assistant) has left it looking like this.

I have heard that spring seeding grass can be a fruitless endeavour, but am unsure how else to fix this. If I were to, I planned on aerating with a fork, raking thatch, adding topsoil and seeding overtop. Is this likely to work, and if not does anyone have any other suggestions for groundcover (sowing wildflower seeds perhaps?)

Thanks for any suggestions