I have recently developed white eyelashes on half of one eye but nowhere else and i have no white patches on my skin - what is this likely to be?

White eyelashes: Known as vitiligo or poliosis, eyelash depigmentation (whitening) can be a result of some hereditary condition. My suggestion: see an ophthalmologist (not an optometrist or optician!). I do not think it's serious, but the eye doctor might be able to determine why and, perhaps, offer a way to reverse it back to normal.

Eyelash whitening: Eyelash whitening can occur for no reason at all but it can related to autoimmune disease. See an eye doctor for further evaluation.