The Mountain Eagle, Hitchcock's second feature film, has been lost since its release in 1926, although a number of stills and critical reviews of early showings still exist.
David Meeker, chief archivist at the British Film Institute, said that film enthusiasts have been searching for the lost classic, the missing piece in Hitchcock's oeuvre, for the past 70 years.
"No one has seen the film since the day it was released," he said. "All that has survived is half a dozen tantalising stills of this great film.
"The re-release of Vertigo has prompted us to make a renewed effort to find any print of this long-lost classic."
The Anglo-German production, shot in the Tyrol, tells the story of a young schoolmistress driven into the mountains after rejecting the attentions of the local justice of the peace.
She is eventually given shelter by a mysterious recluse who marries her to put an end to the scandal and who is then jailed on a trumped-up murder charge.
"The search for the film is made more complex because it had two different titles: the British-German version, The Mountain Eagle, and the US version, Fear o' God," said Mr Meeker.
"Because the film was made in Europe there is the possibility that an enthusiast in one of the old Eastern bloc countries, who were not allowed to collect films under the Communist regime, might have a copy under another name.
"It's more than likely that the masterprint is long gone, but there might be a collector somewhere sitting on another copy."
The Mountain Eagle, which was scripted by Hitchcock's future wife Alma Reville, is one of a number of silent British classics which are missing, presumed lost. Until the Fifties, and the advent of television re-runs, "old" films were disregarded by the cinema-going public who were interested only in new releases. Because of this lack of demand, movies - then shot on nitrate stock which easily deteriorates - were lost through both decay and neglect.
But Hitchcock, who directed 53 films, including the classics North by Northwest, Psycho and The Birds, was never worried about his missing movie.
He once discussed The Mountain Eagle with art-director Francois Truffaut, and said: "It was a very bad movie.
"The producers were always trying to break into the American market, so they sent me a Hollywood film star for the part of the schoolmistress who had fingernails out there. Ridiculous."
Commentators at the time appeared to agree to some extent with the master of suspense. A review in The Bioscope, a contemporary publication, said, "the story was lacking in conviction", but referred to "the undoubted artistic merits of the production" and the "at times brilliant direction".
"We can only hope that somewhere in the world, perhaps in someone's loft, there is a version of this film," said Mr Meeker.
"It would be a tragedy if it was gone forever, but we must remain optimistic just in case some possessive private collector is sitting on it."
Mystery of the missing movies
Abandoned in disused film laboratories, buried in foreign archives under different titles, hoarded by private collectors or thrown away by a small studio which has gone bankrupt - these are just a few ways in which old classics have been lost.
The missing movies include:
Murder at Monte Carlo (1935) - Errol Flynn's performance in this, his first British film, drew him to the attention of Hollywood moguls.
The Bells (1931) - a psychological thriller and the first British film with a score by Gustav Holst, the composer.
She (1916) - based on H Rider Haggard's spectacular adventure story about explorers in Egypt discovering a lost city.
A Study in Scarlet (1914) - the first British Sherlock Holmes film.
Films found in the past two years:
Bella Donna (1934) - an exotic melodrama, starring Conrad Veidt and Mary Ellis, found in the Czech Republic film archives.
The Constant Nymph (1928) - the tale of a doomed love affair, starring Ivor Novello, found in a private collection.