In autumn, the weather's usually mild enough for grass to be actively growing and there's adequate rainfall to germinate seed. This make it a great time to get on and renovate your lawn by scarifying and aerating.
Over time a thatch layer - an accumulation of organic matter - develops at the base of grass stems and it's important to regularly reduce this by scarification. Removal is best undertaken in the autumn. This can be done by hand with a spring-tined rake but if you have a large lawn, I'd recommend hiring in a machine.
Next, aerate the lawn. Use a fork to make holes in the soil surface, so allowing rainwater to drain quickly. Avoiding waterlogging allows for an exchange of gasses at the grass roots.
Alternatively, you can use an aerating machine fitted with hollow tines. This takes out complete cores of soil, so reducing compaction. Rake the cores from the surface before evenly spreading a top dressing mix of 70% graded sand with 30% sterilized loam. Work it into the holes using the back of a rake or trulute - a metal levelling grid. This creates a new rooting medium.
Grass continues to grow through the winter, but during colder weather, the plant concentrates on growing at its roots. There are granular feeds available on the market for all seasons, and you need to select the right formulation. For autumn lawn care, a typical nutrient ratio would be 6:5:10, i.e. 6% nitrogen (N), 5% phosphate (P) and 10% potash (K). The addition of iron at about 6% helps to harden the turf against disease and provides some moss control. Don't over-apply nitrogen at this time of year as it risks producing lush growth that's susceptible to disease.
Later in the year we do get warm spells when the grass puts on some growth and it becomes necessary to top off the grass on a high mower setting - but to avoid damaging your lawn, choose a dry day if you can.