I looked through the pictures in my copy of "Compendium of Raspberry and
Blackberry Diseases and Insects" for something that looked like Ginda
Fisher's description. The only match seems to be Rose Scale. "Small white
circular structures on the cane but may cover much of its surface. These
scales generally occur at the base of the cane but may cover much of its
surface. In severe infestations, the scales may overlap and completely cover
and encurst the bark, causing the cane to look white-washed".
If that's what it is, control is listed as removing and destroying canes,
liquid lime sulfur in dormant season, and standard insecticides. "The
elimination of wild brambles near cultivated plantings may also be
beneficial."