Being in a clay area (hence London Bricks presence in the city) our garden has extremely poor drainage and moss is a big problem.
Add to that I'm not a very avid gardener and weeds get in the lawn and spread. My lawn, while green, if heavily inhabited by moss and weeds Last year I put down moss and weed killer and while it leaves fairly patchy grass, feeding it through the year gave us the best lawn we ever had. Just a bit of moss in a particually wet spot of the garden just now, that'll get treated soon.
Regular weed and feeding is the thing, and it's easy.
This is by far the best combined weed/feed/moss killer, with both rapid greening feed and long term feed. One application a year leaves my lawn weed and moss free for the season.
https://www.lovethegarden.com/uk-en/product/miracle-gro-evergreen-complete-4-1-7kg-bag
plus a spreader:
https://www.lovethegarden.com/uk-en/product/scotts-evengreen-drop-spreader-1-unit