Centaurea common cornflower, once flowering is over cut those stems back, in next to no time a lovely flush of foliage will spring up and you may get repeat flowering.

Is it mildew?

Looks like mildew. Is it just on lower leaves?
Snipping off affected leaves will help airflow & reduce the spread but it will likely clear up with some dry weather eventually...

Centaurea montana, perennial cornflower and mine tend to get mildew too as the flowers go over. Maybe it's the time of year or the weather.

It is the lower leaves only. Ones at the back next to a confer hedge. It has been a very dry, warm spring up here. Followed by unsettled weather. But we have had much worse. :) So I am surprised that this is the first time that I have noticed mildew on the plants.

I'll snip the leaves off and see if it spreads.

Some plants,eg Pulmnarias,are susceptible to mildew in very dry weather.If these are the same maybe this wet weather will stop it spreading further.

I usually get mildew on mine but for some reason, this year they seem to be free of it. I would suggest that you just leave them alone as it is possible that even though you trim the infected leaves, mildew will just return.

Actually discovered this morning that the mildew is much more widespread than I originally noticed. So, I am leaving it for this season. The only real alternative would be to cut the plants back completely if I was to try to remove the infected leaves.

Once the mildew gets going, it spreads quickly. I lost my cucumbers. You can control it with baking soda mixture

To control powdery mildew on plants, mix together the following:
1 tablespoon of baking soda.
1/2 teaspoon of liquid soap.
1 gallon of water.

https://www.thespruce.com/baking-soda-for-controlling-powdery-mildew-1402520

Thanks, Bathgate. That's helpful. I may treat some of the plants around it.

+1 on Bathgate's recipe. A bit of thinning for airflow still seems a good idea though

If it were mi em Id cut it hard back. I do this with my pulmonarias every year. Centaurea is such a toughie, I’m sure it would respond well to being chopped.