Fifty hours of footage from the programme were lost - including appearances by the Daleks - after the corporation reorganised their film library in the 1970s.
"Some shows are the Holy Grail of Doctor Who," fan Ian Levine, who has worked with the BBC to help to track down some episodes, told The People. "I have been on a quest to find all the missing 16mm films since the 1970s when the BBC burnt some of the originals. I'm sure they're out there."
A spokesman added, "We're making strenuous efforts to find the tapes."