I appear to have a fungus on my cucumber plants.
What can I do to cure this?
Are there any cures or organic remedies?
Sounds like either Powdery Mildew or Downy Mildew. If its Powdery (white powdery growth on leaves and twigs) then you can spray with Sulphur or Lime Sulphur. If its Downy Mildew (small light spots or white downy patches under leaves) then spray with Mancozeb or Zineb.
Here's a link to the products in the Garden Shop that treat diseased plants:-
https://www.gardensonline.com.au/Shopping/GardenShop/Category_91.aspx
But if you want to be as organic as possible then try a mixture of 40% milk and 60% water, this tends to work very well in many circumstances and avoids adding more harsh chemicals to the environment.