Advice for lawn upkeep

Hi there!
I'm new to the intricacies of lawn upkeep and wondered if you had any advice for a few issues I'm having.
The main issue is that the main breed of grass just doesn't seem to be growing. See the image below with the browner bits and the lighter green bits. This is at something like 6 weeks since the last time I mowed it, and there's just not much growth there at all. I live in Hertfordshire, we've had a fair amount of rain in recent months. Any thoughts on how I can encourage it best?

The lusher, thicker, darker green areas in the photo seem to be a different breed of grass to the lighter and yellower/browner bits. A close up is below - it seems to be a much coarser and tougher blade, and has stems as well. Any idea what sort of grass this is likely to be? Does anyone recommend this type of grass? If not, what would be a good way to replace it with the more typical, softer lawn grass?

I also have one area of a much wider, flatter leaf grass. Any thoughts on this? What type is it, is it desirable, ways to remove if not.

Many thanks for any advice you can give!
I'm new to the intricacies of lawn upkeep and wondered if you had any advice for a few issues I'm having.
The main issue is that the main breed of grass just doesn't seem to be growing. See the image below with the browner bits and the lighter green bits. This is at something like 6 weeks since the last time I mowed it, and there's just not much growth there at all. I live in Hertfordshire, we've had a fair amount of rain in recent months. Any thoughts on how I can encourage it best?
The lusher, thicker, darker green areas in the photo seem to be a different breed of grass to the lighter and yellower/browner bits. A close up is below - it seems to be a much coarser and tougher blade, and has stems as well. Any idea what sort of grass this is likely to be? Does anyone recommend this type of grass? If not, what would be a good way to replace it with the more typical, softer lawn grass?
I also have one area of a much wider, flatter leaf grass. Any thoughts on this? What type is it, is it desirable, ways to remove if not.
Many thanks for any advice you can give!
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Posts
Set the blades high on you mower and go over the whole lawn. Cutting high leaves more leaf area to feed roots and beef them up for better growth in future. Then you need to buy or hire a scarifier and work that all over the grass. They're like a lawnmower except that they have spikes which lift off thatch from old grass cuttings and weeds and thus allow air aln light to the roots.
Normally this is done in April and September but in your case I think it's worth doing now. It will look scruffy afterwards but have no fear. It will help the grass grow better.
If you have rain forecast you could apply a general lawn feed but make sure you follow the instructions for dosage rates.
Then just keep mowing it high until September when you can apply a weed and feed. Keep the grass at the higher cut till next spring when you can review its need for a weed and feed.
If you have moss or puddles that form when it rains you will need to address drainage and that is done by spiking the lawn with a good garden fork to adepth of several inches and wiggling back and forth to widen th eholes. This needs doing every few inches over the whole lawn. Then you brush on a mix of sharp, dry sand and lawn fertiliser which sinks into the new hles and improves draiange and fees the roots.
You've convinced me to buy a scarifier. Never though I'd see the day!
Did you have any thoughts about those two kinds of sub-optimal grass that I highlighted?
As for the funny grasses - see my first sentence above.