There are miticides available for the treatment of this pest. Destroying plants by burning is also a good option.

North Carolina State University has a good discussion of Broad Mite. The following link discusses cyclamen and broad mites: http://www.hort.uconn.edu

This page has a list of recommended chemicals to use for control of cyclamen mite - broad mite can usually be controlled with the same regime:
http://www.ipm.ucdavis.edu

Sclerotinia rolfsii. Also known as Delphinium blight in the USA. It is difficult to see the small (1/16 inch dia), light brown fungal fruiting bodies, or sclerotes, lying on the top of the soil at the base of the plant in this bad scan. There is also a very vivid white fungal growth (mycelium) growing on top of and through the soil around the plant.

Collapse of the plant is rapid with this disease and irreversible. From first sign to total collapse -- just a day or two.

Destroy plants by burning and disinfect the soil. Grow the delphs elsewhere. This disease is often spread by dispersing infected soil via garden boots and implements.