I saw an advert for "English Spoken Classes". While reading it, I thought that it was incorrect and should instead read "English Speaking Classes". A quick search on Google returned results for "Spoken English Classes".
Is the phrase correct?
You are correct with English Speaking Classes (this has the same meaning as Spoken English Classes).
English is an adjective that describes the type of speaking, and speaking is an adjective that describes the type of classes.
For the words English spoken to make any sense at all, you'd have to insert a colon (or possibly something similar) in the middle to connect the words: English: spoken.