OK, that first picture (the one with the red poppies) looks like someone has sown a meadow mix. This could be a great way of achieving the look you want. The only word of caution I'd sound is this: a lot of people think a wild flower meadow is a low-maintenance option. That's not necessarily true. Yes, you pretty much leave it to do its thing all summer, but it will need cutting, and it will need resowing, weeding and replenishing in the longer term (thinks like yellow rattle can help, as it's parasitic on grass). Otherwise, the grass will take over.
The second picture, with the lillies, is very different. Here, someone has planted lots of little plugs of plants of perennials together. I am a bit suspicious of it, because if you look at the placing of the plants it looks slightly photoshopped - however, this could just be a result of seeing the picture really small on Mumsnet! Anyway, the effect can easily be achieved by putting together lots of different things. The challenge is to keep it looking good year-in, year-out because plants naturally want to grow and clump up, and this effect is basically about preventing them from doing that - so constant division and replacement will be needed. A restrained colour palette is also pretty important. Also, bear in mind that, where you have a lot of things that are out together in late summer (as in that picture), it will need some effort to stop it looking like a non-descript sea of greens the rest of the year, and the whole thing will die back to virtually nothing over winter and look quite bare.
The third picture, with the nigella growing through alchemilla, is actually more clump planted. You have just two things that contrast strongly with each other and flower synchronously planted to trail through each other. I think it's easier to achieve a really good effect with this in a small space - it's clever and controlled. Sometimes I think that gardening is like co-ordinating a year-long firework display. You want a variety of coordinated big bangs that come pretty incessantly, and this is one way of doing that. You might find Christopher Lloyd's book Colour for Adventurous Gardeners inspiring if you like this - it is full of lovely illustrations of similarly bright combinations. This kind of style is also easier to achieve, and lower maintenance than the second option, because you're working with the natural tendency of plants to form clumps.
Note: for both option 1 and option 2 you need sunshine, ideally a south-facing garden that isn't on heavy clay!