Firstly, bee and butterfly seed mixes are not usually exclusively UK wild flowers, they include wild flowers from elsewhere in the world. But setting that aside:
There's basically two types of management regime which make sense in the average garden, pasture/hay meadow, and arable (cornfield).
Cornfield is easier to establish in the average garden with rich soil, and is what most packets of "wildflower seeds" emulate. They are mainly annual flowers, growing from seed each year, and in order to succeed, they need bare soil, not soil that has already been occupied by other plants. So in winter the soil will be bare, and until you've built up a good seed bank you will need to re-seed each year.
Pasture/hayfield is basically grass with perennial plants. Easiest way to establish is to strip off the top few inches of rich soil (you need to keep nutrient levels low as the grass is better at using high levels of nutrient that the plants), then plant a meadow mix which includes grass. These usually include a few annuals to give the "wow" factor in the first year while the perennials are establishing, but the annuals won't persist.
Each year you need to mow up till about the beginning of May and take off the cuttings, then leave it to grow. The ideal is to mow the grass at its peak, in late July, before it starts to die back and return its nutrient to the soil, but that will mean cutting while flowers are still in bloom, so in a garden you'll probably delay the cutting till late August. I wouldn't leave it much longer than that.
In winter, it will look like turf with a mixture or grass and wild flower plant leaves, although some of the plants will die back completely over winter. It'll stay looking a dense green cover. (In summer, it's multilayered - if you do a survey on flower-rich grassland in summer, counting the percentage cover of each species, your total is always way over 100%).