We always get some mildew in early summer, but periods of hot weather usually stop the continued spread. Not this year! Mildew doesn't really harm a healthy, vigorous sycamore tree, and there is no practical treatment for a large plant. Powdery mildew is host-specific: the type you get on your sycamore tree is different from the type you get on your rose bushes. So you needn't worry about cross-infection in your garden. If you are selecting a Platanus, look for hybrids that are resistant. Bloodgood is resistant to anthracnose, but not to mildew. Columbia variety, becoming more common in the trade, is resistant to both anthracnose and mildew.
Powdery mildew on a plane tree