London is full of plane trees (click for Wikipedia entry) and in spring and early summer these shed seeds with attached fibers. In a particularly heavy shedding session, such as a dry windy day, the air in the park can be filled as though with snow.
These fibers are very painful in your eyes, and make you cough uncontrollably when breathed in. Make sure you wear wrap around sunglasses, as this makes a huge difference to your comfort! Tonight I was just wearing my spectacles, and a lot of these fibers went into my eyes. Not fun!