I grew a real nice lawn from nothing this year. The ground was really shite but I just put down the cheapest B&Q seed and it grew beautiful. I then used too much evergreen complete and burnt it in patches
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To be fair though it is almost cheaper to buy turf. You should put down topsoil and roller it but if the grass has grown in your current soil just stick it down.
You can just put it over the current grass. Whats the worst that can happen? It will grow through and make your lawn thicker