Hi

If not soggy you can do now but only light scarifying in spring otherwise you can make a right mess for the rest of the year , if really bad do the same in Autumn , once completed you can lightly re seed, ideal time soil being moist and the warmth/light slowly increasing day by day.

This is what I do others may do something different

I did mine last week when the weather warmed up and the soil was not too wet as to compact the ground. I must admit that I use an electric scarifier as I found the spring rake to be a bit of a killer. I did go over the lawn with a spike to let a bit of air into the ground afterwards.