The audience at the Capitol cinema in London during the middle week of April 1926 witnessed an unusually bold declaration of authorship. The opening moments of The Pleasure Garden, touted in the fan magazines as the debut of "the youngest director in the world", contained, under the "directed by" credit, the slanted and underlined signature of the 26-year-old Alfred J Hitchcock. What followed was also – as it would become clear over the decades – signature Hitchcock film-making. The film's first scene gives us a voyeur's-eye-view of a dancer's legs; and then makes us share the voyeur's unease as the look is returned. The Spectator's influential critic Iris Barry scented the "new blood" desperately needed by the ailing British film industry, writing that Hitchcock had "astonished everyone with his freshness and power".

Despite the plaudits, and despite Hitchcock's self-confidence, there was no inkling that his films would be seen in five years' time, let alone 85. Three million Britons went to the pictures every night, and the turnover was fast. Most movies played for half a week before being replaced, with a favoured few lingering in circulation a little longer. Survival was a matter of luck and the market. But next year, if all goes to plan, nine of the 10 films Hitchcock directed during the 1920s will be seen as no one has seen them since their first release, restored thanks to the BFI National Archive's Rescue the Hitchcock 9 project.

Publicly launched a year ago, and yoked to 2012's Cultural Olympiad, the biggest single undertaking in the archive's history is global in scope, but has its nerve-centre on the edge of Berkhamsted, Hertfordshire, in what used to be – and from the road still resembles – a farm. Home to vast air-locked, low-temperature film vaults, and to the personal papers of the likes of Michael Powell and David Lean, "Berko" is a hive of white-coated, clean-handed, obsessive activity.

Now the largest film archive in Europe, it was among the very first. The National Film Library, as the archive was originally called, was launched in July 1935, a few weeks after the release of The 39 Steps. A lowly department of the young and deeply troubled British Film Institute, it started out, in the words of its first curator Ernest Lindgren, 24 years old when he took on the role, with "no films, no equipment, and no money". Most of the silent heritage had been destroyed since the coming of talkies at the end of the 1920s, and so the library comprised, said Lindgren, "scraps of flotsam and jetsam, the wreckage of a vast output of film, which purely by chance have survived the destructive storm of time".

Perhaps because of his success and talent for self-promotion, as well as pure chance, the Hitchcock oeuvre was among the scraps. His first talkie, Blackmail (1929), was one of the Library's cherished early acquisitions. When Iris Barry began to curate the film department of New York's Museum of Modern Art, also founded in mid-1935, Hitchcock's early productions were among the first British films she sought out. Only his second, The Mountain Eagle (1926), has been lost; and after the discovery in New Zealand of part of The White Shadow (1923), a film on which Hitchcock acted as assistant director and editor, one cannot quite write off the chances of it being found.

There was more than one reason for the great bonfire of silent movies. Cellulose nitrate film stock could be melted down for its silver content, it was expensive to store, and it was and is dangerous to keep: it is volatile, prone to spontaneous combustion and inextinguishable once aflame. Sometimes the capricious compound defied expectations and outlived its successor, "acetate" or "safety", which had a tendency to turn vinegary with age. But other times it didn't. Nitrate's unpredictable nature meant that no film, even once it had entered the library, was safe.

While Henri Langlois, director of the Cinémathèque Française – and Lindgren's arch-rival, would show anything that passed through a projector, leaving a trail of ashes in his wake, Lindgren's urgent priority was to copy the most vulnerable films and stabilise the rest. The principles of storage and preservation established by his deputy Harold Brown continue to underpin the work of the BFI at Berkhamsted and at its special nitrate storage facility at Gaydon in Warwickshire.

Whereas Lindgren, head of the archive till his death in 1973, became notorious for his aversion to showing the films in his care, forcing his colleagues at the National Film Theatre to go to Langlois or Barry to make up their programmes, the newly restored Hitchcocks will be seen in every kind of format, on any number of screens, in all imaginable places. Despite the feeling of safety in widespread duplication, however, the question of longevity still hovers over the endeavour. Apart from the ever more precarious originals, all of the many copies will derive from one painstakingly constructed new source, and while safer materials than nitrate and acetate have been devised to bear it, even the best preservation techniques can only hold back the inevitable.

Each reel of each film has its own story that the archivists have to unpick in their pursuit of authenticity. Though some films, such as The Lodger (1926), Hitchcock's first bona fide hit, have come down to the present in a solitary positive nitrate print, others exist in multiple versions, presenting mysteries that require international collaboration to solve.

The conservationists' first step is to establish the definitive opening-night cut. For example, the BFI's own copy of The Pleasure Garden, acquired in 1940, is incomplete, missing scenes that appear in the Dutch EYE Film Institute's print. But the British is longer overall; and the scenes aren't all in the same sequence. To construct a restored print, the conservationist examines the various versions together, frame by frame, on a "synchroniser". Clues are sought in contemporary print sources: the synopses printed in the trade paper Bioscope, held by the BFI Library in London, provide a detailed first-hand account of the film's narrative construction. For other titles, like Downhill (1927), there are holdings in the institute's invaluable Special Collections department – scripts and press notes, though sadly little by Hitchcock himself.

In parallel with this attempt to get the right frames in the right order at the right speed, the archivists also aim to minimise the marks of age and handling – shrinkage and smudges, bubbling and blotching, and the like – sometimes using techniques from the Lindgren-Brown era. One magnificent analogue contraption, the optical step printer, is used to copy damaged reels on to usable stock. It makes possible the removal of long scratches by rephotographing the offending strips through dry-cleaning fluid, a process the latest software cannot replicate.

But of course digital technology has transformed, and continues to transform, film restoration. In three cases – Champagne (1928), The Manxman (1929), and the silent version of Blackmail – the BFI has the fons et origo, the original "camera negative". The same strips of celluloid that passed through Hitchcock's camera at Elstree and across his cutting desk are now fed through a digital scanner, copied using a cold light source, with each of the 100,000 odd frames given a unique number. Once in the digital realm, stored as images of 4096x3112 pixels (about double the current release-print standard), the films are subjected to careful cleaning and minute analysis for colour balance. The object is not antiquarianism for antiquarianism's sake, but a cinematic experience unencumbered by surface noise. In some instances total clarity is unwelcome: great effort is expended making the written title cards consistent in quality with the pictures.

Not so paradoxically, the restored image is also the most modern. As is well known, Hitchcock regarded the silent film as "the purest form of cinema", and never abandoned its principles. The climactic chase sequence of Blackmail, shot at the British Museum with the feeling for architectural space for which Hitchcock's American work became renowned, will appear to audiences not as an "old" film to be condescended to but as a model of action staging.

While maximum fidelity has been the goal of the archivists, the ambition of the curators is to give contemporary composers a free hand in producing soundtracks. Though a tie-in record was pressed up for the release of The Manxman, the films' first audiences would generally have had to make do with whatever accompaniment their local cinema could stretch to. There is room for invention. So far Nitin Sawhney has taken on The Lodger, and Daniel Cohen has scored The Pleasure Garden; Tansy Davies has been commissioned to score as yet unspecified title. All three have named Bernard Herrmann, whose music was integral to Hitchcock's late masterpieces, as an inspiration, and the results promise at the very least to reveal connections between the silent films and the better known works that followed.

The scores are the best hope of making the films new, but as with the wider project, money is tight and will have to be sought from donors if the nine are to be completed. To date a major contribution has been made by Martin Scorsese's Film Foundation. Apart from their wide digital dissemination, the restorations will be preserved on polyester film negatives that, all other things being equal, will last over a hundred years. It is a wonder that the first attempt to produce definitive versions of the films in which Hitchcock honed his style has come in the original materials' twilight years – but that's not untypical of the archivists' world, where firefighting has always been part of the job.

• Details: bfi.org.uk/saveafilm