From Dr Helen Clark, who is having to remove a 50 year old hedge due to this infection:

Thank you for your enquiry to RHS Gardening Advice.The spotting on the leaves of your Kerria, is caused by a disease known as Kerria blight. This also causes lesions on stems and, as you have described, will quickly infect any new healthy stems that grow from the ground.

Kerria blight was first found in the UK in 2014. It is caused by the fungus Blumeriella kerriae. The disease causes severe defoliation and purple spots or lesions on the leaves and stems – girdling stem lesions can lead to complete dieback of the affected stem. This pathogen has been recorded on Kerria japonica previously in America and is now spreading through the UK. I found the spores for this fungus on your kerria leaves and stems. The leaf and stem lesions and defoliation you can see are typical.

We have a web profile on the RHS website: https://www.rhs.org.uk/Advice/Profile?PID=1018 . We have also published a short research note if you would like to read some more details on the fungus: http://ndrs.org.uk/article.php?id=035034# 

The disease is best managed by removing all infected plant material and either burning it or disposing of it at your local council composting facility. Home compost heaps rarely reach the high temperatures which are required to kill fungal spores. 

There are no fungicides available to home gardeners with specific recommendations for use against this pathogen. However, there are fungicides labelled for the control of some other diseases on ornamental plants and could therefore be used legally on Kerria (at the owner’s risk) to try and control this disease. Details of suitable fungicides are given in the web profile mentioned above. It would be prudent to apply a small amount of the chosen fungicide first, at a solution suggested on the packet for other problems, to ensure that the product will not cause damage to the plant. 

Unfortunately this problem does appear to be very difficult to control and a number of my colleagues have chosen to remove their Kerria plants. The good news is that this fungus is specific to Kerria, so other plants in your garden should not be at risk, and you can replant with any other shrub.