Just to sign off on this, a local tree-and-hedge man quickly and efficiently removed the infected juniper down to a low stump and took it away - he said he'd never seen anything like it. I scraped off the top layer underneath (needles and sawdust) and binned it, so I hope there isn't infection in the soil, and I'll look out for any signs of anything else catching it, and use anti-rust spray if so. It seems to be too late to kill the stump this year, but I'll do it next winter if necessary. And I'll plant the bed with stuff that doesn't get rust.

Although Gymnosporangium seems to be common in the US, I can't find much about it in Britain. I couldn't find anything on the internet about how to treat the jelly itself - is it infectious on clothing or the ground? When does it release its spores - continually? It's very unpleasant to the touch as well as nasty to look at and I hope never to experience it again. Thanks to everyone for suggestions.