Posted: 23/02/2017 at 14:54
If you have a puddle that sits there for a long time, you have a drainage problem. If the rest of the area drains well, you just need to build up the dip to level it, but it does sound as if your back garden could be a bit wet. Moss usually grows in damp, shady conditions, but it will also take over when your grass is weak and thin because of poor nutrition. You cannot change the light available, although there are seed mixes which cope better with some shade. Remove as much moss as you can by raking with a lawn rake You can introduce air and improve drainage by aerating and brushing over grit and compost. Seeding the bald bits doesn't seem to have worked so I would be inclined to feed up your existing lawn first. Personally, I wouldn't start with a lawn feed, I would use a general fertilizer like blood fish and bone and see if that helps.
HOWEVER, before you do all this hard work, have a think. Perhaps this area has never supported much grass. Are you flogging a dead horse? You might be better giving up on grass and rethinking the whole space. Good luck,