The presentation of four surviving episodes of a six-part story, "The Reign of Terror", will take place at the National Film Theatre in London.
The story starred William Hartnell, the first doctor, and was originally broadcast in August and September 1964. But the tapes, like many others of the period, were wiped by the BBC and appeals have been made in recent years for anyone with copies to come forward.
The episodes of "The Reign of Terror" were rediscovered during the 1980s but have been seen only at a Dr Who convention and through counterfeit copies.
One episode was returned to the BBC by a private collector in 1982, and three years later that same episode and three others were sent back by a television company in Cyprus. Episode four, "The Tyrant of France", and five, "A Bargain of Necessity", are among 100 or so Dr Who shows still missing.
Roger Clark, an organiser of The Wolves of Fenric, a Dr Who fan club which began in Wolverhampton, said next month's viewing was very important for the enthusiasts. "If nothing else, it keeps the programme in the public eye," he said. "Also there's missing episodes that are still to be recovered and the more people that find out a specific story is missing, the more of a chance it might be recovered."
The story was the eighth in the Dr Who series which began nine months earlier in November 1963. In it, the Doctor and his granddaughter and assistant Susan, played by Carole Ann Ford, travel back in the Tardis to the time of Robespierre's reign of terror at the height of the French Revolution, instead of back to 1963 as the Doctor had intended.
Mr Clark, 30, a writer and broadcaster, said "The Reign of Terror" came from a period when Dr Who had an educational element. Historical adventures alternated with the science fiction which is now more closely associated with the series.
"In the early days, it did do a lot of purely historic adventures which were very, very accurate." The first history series involved the Doctor in the time of Marco Polo's explorations. Teachers recommended the series to their pupils, Mr Clark said. "A lot of people think these historicals are not going to be as good as the science fiction, whereas the reverse is true. The BBC is known for its costume drama so any historical production from the BBC looks good straight off."
Veronica Taylor, the television officer for the National Film Theatre, said: "We do try to show any Dr Whos that turn up because there's always a lot of excitement about them. There's a big audience out there for Dr Who. Obviously the early episodes were very creaky and low-tech in terms of special effects, but in terms of imagination it was always good."
The showing is scheduled for 14 July, Bastille Day, as appropriate to the subject matter.
The BBC has issued many Dr Who episodes on video, but only where the complete set is in existence. However, the sound exists on all the programmes and in August it is due to release a CD and cassette of the original soundtrack of a story called "The Massacre of St Bartho-lomew's Eve".
The very first 13 episodes of Dr Who survive, but the next seven are missing. The programmes are then again extant until the missing two from "The Reign of Terror".
Although the television series ended 10 years ago, a BBC spokesman said there was still huge demand. It publishes two books a month and a video of the old series every other month. And earlier this year, a missing episode from 1965, called "Crusade", was bought at a New Zealand film fair for $5. It and another episode, "The Space Museum", has just been released on video.