Moss can be an indicator of several things. These include poor soil (nutrition). Moss does not compete with healthy grass. Feed the grass! Poor drainage. Poor light (unlikely on an airstrip but then you are a long way North), acidity - or rather incorrect Ph for good grass. If you were re-sown recently you may have used a grass type unsuitable for your soil.
First you need to identify which of the above (or any other reason) is why it has taken over - easier said than done - and correct it. Then you almost certainly need to spike the ground as said above twice per year. Then mosskill perhaps (Sulphate of Iron is relatively cheap and works a treat) and scarify the drifts of dead moss you'll then accumulate and burn it. And probably keep doing this for a number of years until you're on top of the problem. Overseeding with a more durable grass type might help too.
Moss is tenacious and a real pain to get rid of I'm afraid. It takes a lot of effort and above all a long time to achieve a result. Once sorted you may need to keep repeating the treatment to keep it at bay.
The RHS will have plenty of good technical advice, as will sports pitch care websites. Perhaps first best to try asking groundsmen at your local sports fields/golf clubs, they should have good skills in this as well as local knowledge. (and maybe the tools available).
Seaweed extract sprayed on my lawn worked wonders but none of these remedies works in isolation, you'll need to attack on several fronts to make headway.
Last edited by noflynomore; 13th Dec 2016 at 17:04.