I have a few mossy areas too, mostly in shady areas and after such a damp year. Some people say it suggests acid soil but I am not sure of that and have never found it a problem: one year I scraped some off to compost but now I leave it and it just comes and goes a bit. A light hoeing in dry weather reduces its vigour.
How has your no dig plot been this year Darren? I have the impression from my experiment and comments of other gardeners that unisturbed soil has enjoyed a good year in compsrison to dug soil.