With all the wet weather and lack of sun grass tends to languish whereas moss relishes the conditions. When it comes to the first cut of the season this will be apparent with a springy surface and large patches where no grass is growing.
Stage one to remedy this is to spread a standard Feed, Weed, and Moss Killer. Having been watered in by rain the moss will quickly turn brown. Time now to go to Stage two, scarifying the lawn.
I used to hire a scarifier every year to do this which was a heavy petrol driven machine which did a good job. Hire prices rose to the extent that it looked to be cheaper to buy a machine to do this chore, and the one I chose was the Flymo Lawnraker Compact 3400. I also bought some spare tines.
The machine is a little plasticy and appears fragile. However it has now lasted several years and so has paid for itself, and it does a good job. Tines need to be checked regularly as they are the working part of the process and undergo a lot of strain.
The electric motor spins at a fast rate and the fragile looking tines rapidly move the thatch of the lawn to the collector, which fills all too fast (no complaint here). It is necessary to have a supply of bin liners which rapidly fill as the machine is efficient. I can then take the moss to the Civic Amenity Site where it is turned into compost.
I recommend this machine if you have a typically sized garden as it does a good job.