Terrible lawn…help please

I’ve lived in my new build for 4 years and I don’t know what to do to with my terrible grass.
I’ve tried scarifying and seeding (just generic seed from garden centre), but these bare patches never improve.
These areas are mostly in the shade, and the ground is very heavy and wet.
I have 2 small dogs so unsure what is safe to use.
Also is it too late in the year to try to fix this?
Any help and advice would be massively appreciated

 

Thanks for the reply. It’s an area that is never walked on, other than to mow the lawn.
It’s never been dry. It has always been thick, heavy, wet soil.
The lawn also has literally hundreds of little mounds of mud (I’m guessing worms) and lots of mushrooms