Winter Lawn Care

This is my first garden, so my experience is limited.
The lawn in our new house is not looking as good as it was.
I know it is winter and maybe it's normal at this time of year, but I wonder is there anything I should be doing now to aid it's recovery.
Should I still be cutting the grass in Winter?

I did spike the soil and apply an autumn lawn feed in early October, but there seems to be a lot of dead grass now. It's not down to lack of water, as there has been plenty of rain.
I've attached some pictures from April and now for comparison.

 

I would mow it now but on a slightly higher cut than you use during the summer. Give it a few weeks to recover and see how it looks then but don't feed it again before next spring.

 

Remember not to cut more that one third off the total length of the grass. looks like it might be a bit thin when its cut.

 

@Hammer2001 - Your lawn looked spectacular with the stripes in the first pics but a lot of rain (it has been a very wet winter) which doesn't help and may overwhelm certain types of grass. If you have and dogs peeing on it or kids trampling on it, it will make it look rough at this time of year.

Also has it become so long that it's keeled over and bloced the light from the surrounding grass?

However, there are large areas of yellow or dead grass and this may indicate an infestation of leatherjackets (daddy long legs larvae) or chafer bugs. It may be worth buying some nematode treatment that targets both and spray this stuff as well as a fertilizer in the spring. Maybe you could also put some more more seed in to thicken it up.

The grass may recover on its own eventually but if there are bare patches, they are an open invitation for weeds to appears, so make sure any bare areas are seeded, even now.