Reddit reviews Doctor Who: The Return of Doctor Mysterio

You can buy the episode on Amazon or iTunes for a couple of bucks. That's what I did.

It's available for download on Amazon. I hope it works.

https://www.amazon.com/dp/B01MQOFKRV/ref=cm_sw_r_tw_dp_N-uwybVR1D6JT

Here's for Husbands of River Song in season 4
https://www.amazon.com/Doctor-Who-Husbands-River-Song/dp/B018MJAMQM

Looks like Mysterio isn't included with Prime
https://www.amazon.com/gp/aw/d/B01MQOFKRV?ref_=aiv_dp_season_select

They're both under the title ' Doctor Who - Christmas Specials' instead of plain DW