Separate shots show the actor flanked by apparent bodyguards in a crowded harbour area.
The series is set to include a storyline featuring the budding romance between Prince William and Kate Middleton, who met in 2001 while they both studied at the university.
Actress Meg Bellamy will play the young Princess of Wales.
Production was originally due to begin in August but was delayed following the death of Queen Elizabeth II.
Netflix, which produces the show, has been approached for comment.
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