The 10-year-old recently filmed his scenes for the sci-fi drama in South Wales, according to This Is Wiltshire.
Strefford did not film any scenes opposite Who star Matt Smith, but his character is said to reappear in the festive episode as an adult, played by "a well-known actor".
Other stars confirmed to appear opposite Les Misérables star Strefford in the instalment include Richard E Grant (Withnail & I), Tom Ward (Silent Witness) and Liz White (Life on Mars).
New companion actress Jenna-Louise Coleman will also return to Doctor Who in the Christmas episode, after making a surprise appearance in series seven premiere 'Asylum of the Daleks'.
Doctor Who continues this Saturday (September 8) on BBC One and BBC America with 'Dinosaurs on a Spaceship'.