If you click on the bottom icon which says cc (closed caption) it offers you the option of what language you would like in the tools. But QM and CPss Mary and Pss Benedikte are speaking in English throughout. another fun one in the Uncrowned Jewels of Wallis, Duchess of Windsor https://www.youtube.com/watch?v=BdJaURVZ7uI
Hmm I couldn't get the option to come up - I'll have to try again. But you're right, it's great hearing the royals speaking in English (if a bit strange, I just assumed they would be speaking in Danish for a docu on Danish television). I realized as I started watching I've never actually heard Danish being spoken - I was struck by how German it sounds (I don't feel it "looks" German when written out, if that makes sense).