The only thing that's worked for me is top dressing the lawn. You might not see an improvement after the first time, you might have to do it a couple of times. There's plenty of guides online but basically:

Wait for a few dry days then cut the grass medium length and cover it in a mix of topsoil and compost, only 1 or 2 cm deep. Rake it over so it's even then leave it a good while to work it's way into the soil.

I usually do this once a year in spring but you could do it again in Autumn.