Well naff we don't get Greenfinches in our garden anymore,and we used to have a garden full,
any ill ones I see are at my lottie where I grow masses of sunflowers.
this year I've seen three Greenfinches and one was ill, fluffed up and on the ground, and couldn't fly,heavy breathing and drooling saliva
last year I saw one also on the ground with the same symptoms, which I believe is a disease called trichomoniasis, see the RSPB website for more details, hope this helps / shades x