Prince Philip actually hated being filmed.
This episode correctly depicts Princess Alice making the Sign of the Cross following the Orthodox Church (prominent in Greece) style instead of the Latin Catholic style. The Orthodox style is first right shoulder, then left; while the Latin Style is first left shoulder, then right.
Princess Alice of Battenberg (later Princess Andrew of Greece and Denmark) left Greece for the last time in April 1967. She spent her remaining years living in Buckingham Palace where, despite being lucid but physically frail, she died on December 5th, 1969, aged 84. According to her wish, her remains were transferred to her final resting place at the Convent of Saint Mary Magdalene in Gethsemane on the Mount of Olives in Jerusalem. For hiding and saving the Cohen family during WWII, she posthumously received the honorary title of "Righteous Among the Nations" from the State of Israel.
In "Bubbikins (2019)," Princess Margaret says, "This is like some kind of nightmare Christmas." Princess Margaret is played by Helena Bonham Carter, who was in a long-term relationship with Tim Burton, the writer and producer of the movie "The Nightmare Before Christmas (1993)."