The copyright exception for education allows all types of sound recordings from the internet to be played during lessons and for the illustration of teaching, provided the recordings on the internet are there legally and are not infringing copies. If the podcast is on a subscription-only channel, the teacher can use their own access under the exception but it would be preferable to your school/college to have its own subscription so that usage data can be ascribed to the institution.
As a teacher, can I broadcast a podcast to my students during a lesson?
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