Wild area in lawn

Well done on trying it out! There are wildflower mixes available especially for bare patches of soil. some of the plants you list may not work out in a lawn situation. Poppies are annual, but realistically they will only flower in the first year, they need to have the soil turned to flower every year (why you see them growing as weeds in fields of cereal), foxgloves are biennials, meaning they need two years to flower ( so you can't mow them at the end of the first summer because they need to hang onto their big leaves), and bluebells and snowdrops like to be under trees or shrubs.
I leave parts of my garden uncut from April to October and, interestingly to me, more and more species have started growing over the years with only a little interference from me- and this year I ended up with two random wild orchids for the first time. So, if I could suggest you get some cowslips (not picked from the wild!, potted ones available early next year), and start gathering red clover flowers when they start to turn brown, along with oxeye daisies ( the really big wild daisies), rake the area after it is cut- really scoring the ground and scatter the seed in. You can start adding things like this over the years- the grasses will always dominate, but the wild flowers will survive (all this in my opinion of course).

Don't bother trying to plant snowdrop bulbs in autumn, wait until spring and buy a few pots of snowdrops in flower, or at least with green leaves, dig out a small hole and pop in the contents of the pot. They are more likely to grow from 'green'.

There’s a website called http://wildflowers.ie/ which I find excellent. Unfortunately the site has closed down and they are redesigning it and there seems to be a delay in the relaunch. But the old site is still there for ideas and hopefully it’ll be up and running for autumn. I’ve also heard of a company called ‘seed bombs’ on Facebook but I never used them.

I would leave what you have now and enjoy it, then come autumn cut the grass as low as it can go, rake it bare, pull the normal perennial ‘weeds’ ( wildflowers), as lovely as they are they tend to suffocate the other flowers. As Harry Palmr said buy yellow rattle, but this can be got through the wildflower seed mixes. Go easy on it though if your wild area is near a proper lawn. Yellow rattle is very beneficial to wildflower meadows because it’s parasitic on grass so if it escapes your wild patch you could end up with a patchy lawn too.

I left a circle of about 8 foot of our garden uncut this year just to see what would happen naturally, the grass and weeds are about two feet tall now. There's a rose plant at the edge of it that has flowered away as normal and there's a nettle plant in there.

It's visible from our bedroom window and the one thing that can't be missed is the amount of small birds that feed around the edge of it and inside it every morning. It's like a tiny little nature reserve for them. The chickens love it too, usually they feed around it in the afternoon or just go inside and lie down for a cool rest in there on a hot day.

If you don't want the yellow rattle to continue in your garden cut it before it goes to seed. Its an annual so it will just stop.

Drop some daffodils and tulips in to the area to.
They will add some spring interest and die back before everything else gets going. I've a 15x10m area done with them. But it's under two large willow trees so can't do a whole lot with it during the summer. I just let the grass and weeds go wild. (Not all weeds mine you)