Wow! A Giant Groundsel (Dendrosenecio)?! I had no idea that anyone was selling them, or that they would even grow in the UK--or anywhere outside their native environment! Do you have pictures?

I think, Tugbrethil, Steragram might mean Senecio, now called Brachyglottis - felted grey leaves, evergreen, about 3/4 feet high, yellow daisy flowers in summer?
Usually, Steragram, that white stuff you've found is some form of mycorrhizal (spelling?) fungi and isn't always harmful, but its much more noticeable in bone dry soil. A photograph of the shrub concerned would be helpful, but sounds like you've already dug it up, so a photo of the site where it grows would be useful. Otherwise, what situation was it growing in - near conifers? in full sun?, that kind of info if you can't manage a pic.

Ah! Thanks, Bamboo! We don't grow those here, but those fungal threads sound like common decay fungi, that help recycle dead roots into the soil. My reading makes them sound like plants that need excellent drainage, and possibly a more mineral soil. If it was in a heavy soil, and/or in an area that was periodically saturated, it may have been afflicted with one of the many collar rot fungi, which tend to kill one branch at a time. Solution: ensure fast drainage, and direct runoff away from the area.

Yes Bamboo, it was a brachyglottis - I can never remember the name. It was growing in a dry spot under a conifer, so drainage was certainly not a problem. I cut the branches which died to see if there was any indication of staining but there wasn't. I disliked the shrub and am quite glad it has gone, but was concerned about replanting something else in the same spot. The white threads were not like normal mycelium as they appeared as single strands an inch or so long here and there, but not connected to each other. They looked rather like very new rootlets, but were not connected to the roots in any way.
Maybe it just overheard me rudely calling it giant ragwort and took offense!

It's because its near conifers - that's why I asked specifically about them possibly growing near. They take the water from the soil, not much left for your Senecio (or anything else you plant there) and then you notice the mycelium threads, which often are found in association with conifers. Sounds like you need to think about planting a little further away from the conifer behind when you consider what else to plant. As for the name brachyglottis, I find it hard to forget, but wish I could, what an absolutely dreadful, appallingly unattractive name it is, lol.