Lawn is dieing on me :(

I spent many happy days this summer on my hands and knees digging up the back lawn, getting rid of lots of thick moss and weeds that had turned the back lawn into more of a weed bath than grass. I planted new grass seed which came up very well. I waited a good 1.5 months before I trimmed the new grass, and almost 2 months before I put down some fertiliser recently. In hindsight I may have put too much fertiliser as was guessing and I may have trimmed the grass too low but unsure on all that.

Even before I put the fertiliser down though, there were signs things were not going well. I was sure I saw the grass in patches looking less healthy and little clumps just dying. There was also a problem with a small animal digging up the new lawn sections (only very small bits) all over which basically put pay to the new grass which was not going to perk up ever again after that.

Over last month the brown and dead sections have got more prominent and I think they'll be more before end of the winter.

This back lawn has never been great and suffered from lots of weeds and less stimulated patches over many years - lots of it doesn't get a lot of sun and it can get waterlogged. It looked great after I finished my work but now a few months later it's looking once again like it's not happy.

Any suggestions on what I might have done wrong or the best thing to do over winter and then have another go next spring to perk things up? It might be that things recover naturally over winter but what should I do to give it the best chances?