The bird was an adult male looking very lethargic an allowing me a very close approach, it's plumage was scraggy looking puffed up and it appeared to be constantly gasping for air. Exactly the same symptoms I had witnessed in the earlier bird which also showed matted wet plumage around the face and the beak.
Being concerned I investigated on the internet and found out exactly what the problem is.
Looking on the excellent RSPB site they had a page on the Trichomonad parasite that is killing Greenfinches in gardens, apparently the parasite lives in the upper digestive tract of the bird progressively blocking it's oesophagus eventually killing the bird through starvation as the food it tries to digest cannot be swallowed/ digested.
Nothing can be done sadly to cure the bird.
Apparently the only thing that could be done (according to the RSPB ) was to clear all the finch feeders, disinfect them, clear bird feeding surfaces and not feed the finches for 2 weeks. This is to discourage birds from feeding collectively and therefore pass on the parasite from the infected bird or it's saliva/ excreta to another host.