Cedar apple rust is one of the gymnosporangiums, like Pear Rust - it starts out on Juniper but needs to complete its life cycle on Pear or Apple, depending which particular variety it is. If yours is still at the canker/gall stage (this is how it overwinters, in this form), you can manually go over the plant and pick those off - if its already produced the yellow thready stuff, then its too late, it's at the stage where spores are being produced which will be trying to find an apple or pear tree. You can try using a fungicide, but none profess to act on this particular form of rust infection. I'm assuming there is an apple or pear tree within a quarter of a mile, and if so, its usual to remove one or other plant to prevent a continuing problem, though most people are more concerned to protect their fruit tree than the juniper.

Thanks for that Bamboo - a little more information than I previously had. I live in a residential rural area - almost everyone near has at least one apple tree - including me! Since posting this I have removed and burned the two rather large juniper bushes concerned - yellow gunge and all. I will spray the apples with a copper fungicide and advise my neighbours to do likewise.

Copper fungicide may do nothing at all against this particular infection - if you can get hold of some Westland Plant Rescue Fungus Control Concentrate, that should work, but it was withdrawn in 2014 - anywhere that's got any can sell it up to end of June this year. Otherwise, Bayer Systhane Fungus Fighter Concentrate may have some effect; this one will be withdrawn in November this year, but can be sold up until end of November 2016.

Thanks again Bamboo. I don't buy Westland products on a principle that I won't go into here but I will try to get hold of the Bayer product.