Reduce the frequency of mowing now and towards the end of the month. Scarify (rake out the old dead grass and moss) by hand (hard work!) or with a machine, spike to improve drainage again either by hand with a garden fork or with a machine, add a top dressing of soil/sand/compost mixed according to your soil type (ask for advice at your local garden centre if you are unsure) and feed with autumn lawn feed. This low-nitrogen feed strengthens grass in preparation for winter; do not use spring lawn feed as this encourages grass to grow and it may not survive the cold. After all this your lawn will look dreadful, but fear not, it will benefit enormously from the regime. Repair bumps, hollows, bald patches and broken edges too.
Now is the time to start making a new lawn. Good preparation is vital whether you are laying turf or sowing seed: remove weeds and stones, dig over thoroughly, adding organic matter and fertiliser, rake smooth, firm by walking up and down and rake again at right angles, repeating the raking and firming process until the area is flat and the surface is a fine crumb texture. Sow seed according to the packet instructions and lay turf in a brick pattern so no joints are in line. Water well and keep off for 4 to 5 weeks.