Hi Moss is caused by a few problems and to stop it you should address the problems which apply to your lawn!
Shade, Dampness, scalping the grass down to the soil when you cut it. poor grass cover, lack of nutrients for the grass.
This is a good time to start looking after it.(the lawn) So. Remove all the problems/causes i have listed.
Treat the lawn with a good dose of Iron, wait till the moss goes black and then scarify it and mow up the arisings.
Loosen the soil to create a tilth and re seed it. You could try top dressing it with SHARP sand.
You could hire the equipment or visit your local sports club/golf course and ask if there is anyone there who could help out (for wages of course)
If you look in the press there are specialist firms but some are poor.
Tell them what you want and get them to give an estimate and and ask them to write down what they will do.
You have to get a dense sword to out compete the moss and in spring and late Autumn apply lawn sand (which contains iron)
Some people think that lawns are there just to be mown and that is all but the truth is you'll get much pleasure from creating a nice lawn and caring for it.
Finally and very important is to check what the soil is like. You need a decent depth of good soil ,6 inch or so, for the grass to thrive. If you hav't then start again from the bottom.
I am going to do this for a friend. Dig out all stones and runnle into a skip and import good soil in its place then re-seed etc. Not easy but there are NO short cuts.
Chris