I'm afraid its a fungal leaf infection that Yucca gloriosa in particular are prone to getting. Unfortunately, there are no longer any useful fungicidal treatments that might help, although neem oil spray (if you can find it in the UK) may have some effect if used frequently. Using any fungicide you can find (Bayer fungus fighter or similar) in spring may have some effect in preventing it getting worse.

It might be worthwhile looking for bacterial fungus fighters, such as Streptomyces lydicus, or Bacillus amyloliquifaciens.