Thanks to a notice from an anonymous commenter, I am thrilled to report that the film “Greek Papyri–The Rediscovery of the Ancient World” is now available on Youtube. The film was produced in 1971 by the Greek and Latin Departments and the Slade School of Fine Art at University College London. It was directed by Mirek Dohnal and features some fantastic archival footage of the British papyrologists of the day. The film is mentioned in an exhibition catalog by T. S. Pattie and E. G. Turner, The Written Word on Papyrus: An Exhibition Held in the British Museum 30 July – 27 October 1974 (British Library Board, 1974).
The quality of the production was excellent. Eric Turner’s obituary in the Proceedings of the British Academy described the film as follows: “. . . in May  came the première of Mirek Dohnal’s film Greek Papyri (Turner had suggested the subject to the head of the Slade Film Unit; he and his pupils and colleagues starred, with Zauberflöte in the background, and many hours of patient labour; the film won a silver medal at the Venice Festival) . . .”
There are a number of fascinating things in the film, including some interesting video of the sorting and flattening of Oxyrhynchus papyri and some footage from the 1960s of the dismantling a mummy mask using hydrochloric acid (at about the 25 minute mark).
[UPDATE 16 March 2019: See identifications of some of the people featured in the film here.]