Lawn advice

Hi all,

My lawn has taken a battering over the winter - it hasn't been helped that my garden slopes down at the back (a flood mitigation put in by the developer) so holds the water in a winter.

I used to have such a gorgeous lawn by thanks to a neighbour who lets the weeds grow and the weather mine looks a mess.

It's very muddy and soft so hoping to get it dried out but I've now got moss in it as well as the dreadful dandelions. I wonder if anyone has advice on how I can start getting my lawn back to glory. Although I'm due to move house at some point, I won't want it looking bad and want to be able to enjoy the garden in the summer.

I've attached some pictures of the moss. My dad who likes to tinker in the garden mentioned something about white vinegar?

I was going to just strim the grass and leave it for a while to dry out, then cut it and then perhaps use weed and feed and maybe throw a load of grass seed down.

I'm not overly grenfingered as they say but want to start doing more in the garden.

Thanks for reading and for any advice