REALLY want to ID these two plants

Yes - they have captivated me I've got to say .

I've partially micro clovered already but want rid of the grass and build up more clover, have a crack at camomile and maybe these little blue fellas. All I have is one lawn and a large container with hardy perennials so I'm not soooo worried about the blue ones taking over.. I think! I don't think I'll pursue the pink ones.

 

Can I suggest you might like this one as well … another pretty native flower that grows happily in lawns and us very valuable as a nectar source for bees Selfheal | The Wildlife Trusts
So pretty.

 

We have that everywhere here too @Dovefromabove . It self seeds and spread in borders or grass, and I also have it along the edge of the side path. I always leave it, and even if it spreads into the grass edges I don't bother removing it. The mower can catch the flowers, but as often as not, it just goes over it. I expect if people cut their grass very short, it would get caught.
I think if you want more wildflowers than grass alone, you may need to make the grass itself poorer by scalping it and actively sowing seed, or planting out plugs or small plants.
If the grass gets fed, that won't help either. I only really feed my grass in spring, but we're also on clay so it's always a bit stronger growing because of that, and our climate means the grass doesn't readily die off/go brown in summer.

 

That's rather pretty!

 

I have loads of self-heal. I let it flower and then remove the top growth before it seeds. It pops up in the lawn and the gravel.

 

It is a lovely thing … and the dark colours that the leaves can show make it look rather special.

 

I like.

 

Plenty of self heal in my front "lawn" photographed this morning! I've even got a pink variant.
No Mow May is just the start for me. I've now completed Let it Bloom June and will observe a full month of Thigh High July (though actually some of those grasses are up to my chest already). Lots of lovely grasshoppers in amongst that lot.

 

Lovely.

Love it!!