Hi there, i would spike/aerate your lawn, import some quality screened top soil, mix this with sharp sand (40% soil-60% sharp sand) and cover your entire lawn and level the plot with a long plank or similar.
It always pays to fully prepare the soil first incorporating lots of sharp sand or grit for drainage if on heavy clay, get it as weed free as possible and use a quality seed. Depending on the kind of traffic/usage the lawn will have to deal with will determine what seed you should use.
PS. Rigby Taylor is a company i use for all my grass seed. Happy Gardening.