With the exception of the Welsh poppies, everything Errol talks about are perennials which will grow in grassland. Which means you can mow it in autumn but otherwise leave it to its own devices. I've done that in my garden. I have snowdrops, wild daffodils, primroses, cowslips, species crocus, species tulips (they don't look like the usual florists tulips, much tinier, with open flowers), snakes head fritillary, lady smock for spring, then for summer meadow cranesbill, hedge cranesbill, shining cranesbill, common vetch, bush vetch, meadow vetchling, birds foot trefoil, melancholy thistle (no prickles), red and white clover, catsear, self heal, daisies, hoary plantain, creeping buttercup, meadow buttercup, greater burnet, white campion. The self heal, daisies and white clover prefer the path through which I mow every week or so, the rest are happy in the long grass. Some of them are chosen to be specific to my location - damp clay, partially shaded.
It would be easier to have a separate "spring meadow", to be mowed regularly from end May onwards, and a "hay pasture", "grazed" (ie mowed) till end May, then the stock kept out (stop mowing) till you take the hay cut in July/August, then mow again. The important thing is to keep the fertility low, because the grass can use high fertility levels more effectively than the flowers you want to encourage. So it's more important to cut the grass at peak growth, before it starts sending its energy back down into the roots or rotting back into the soil, than it is to wait for the flowers to seed - they're perennials, so they'll still come up next year. And when you do cut, be sure to remove the cuttings.
Alternatively you can emulate a cornfield, with annuals that need clear ground to germinate. You'd have to clear the plot every winter and keep it weed free, then either let the seeds in the soil germinate in spring, or buy a fresh packet. For a truly wild plot you'd use cornflower (the blue wild form), corn marigold, corn cockle, corn chamomile, poppy.
If you're less purist and just want the wildflower effect, you could sow any mixed annuals. Councils use mixes that commonly include non-natives like Phacelia, Californian poppy, Cosmos. "Bee friendly" selections would give the same effect.
If you're still with me, sorry for the length!