You may be better off giving it a good raking. Grab a garden rake and go nuts. This is one way of removing the moss. In my old house I treated my north facing rear garden with some week and feed (something like that) and it looked terrible! The lawn was full of brown patches and looked awful so I ended up re-turfing the lawn. I moved in the summer and my front garden had some moss. Recently I raked it all out. It was pretty hard work but it did the trick. Its surprising the amount of thatch you will get. I had around 2 large black bags full. After I raked the lawn I got some good quality seed and fertiliser and treated the lawn. Its looks rough now but should start to recover in the spring (moss free) You need to aerate the lawn too. Moss is sometimes caused by poor drainage. If you get water sitting on the surface this can encourage moss. Aerating the lawn will definitely help with this. You can grab a fork and go crazy or even better, you can call a company called GreenThumb (Im assuming youre in the UK) and get them to come out and carry out hollow tine aeration on the lawn, this is better than using a fork but it will cost you. I think average size lawns are around £30. Good luck.