Several years ago, I received a strange request from the Heritage Lottery fund. Would I comment on an application to house in a museum a large collection of artefacts used in Hammer horror films from the late 1950s to the 1970s? There was an inventory that included a cloak, some fangs, quantities of Kensington gore (fake blood), designs for castles and laboratories - those kinds of artefact. Did they, or did they not, deserve to be considered part of the national heritage?

I did not hesitate. Of course the material culture of Hammer films deserved a place, preferably a prominent place, in a museum. Why not? The five versions of the Frankenstein story made between 1956 and 1972 (with Peter Cushing as the arrogant aristocratic scientist), the six versions of Dracula made between 1957 and 1970 (with Christopher Lee as the grand saigneur), plus The Mummy (1959, with both of them) and The Devil Rides Out (1967, with Lee as the good guy for once) represented a key moment in the history of British cinema, when after the black-and-white years, film-makers found roundabout ways of telling stories about sexual liberation. They were also in a direct line of descent from the Gothic novels of the late-18th/early-19th centuries, and even from the public image of Lord Byron himself. So, yes, they were a part of national heritage.

One reason why Hammer films made such a splash at the time of their release - strongly disliked by the critics ("depressing, degrading: for all lovers of cinema only two words describe this film," wrote one in the Tribune about The Curse of Frankenstein, 1957; "SO - For Sadists Only," suggested another) and equally strongly liked by the public - was that there had been surprisingly few British horror films before the late 1950s. Boris Karloff and Bela Lugosi had made one or two in the 1930s (not their finest hours, sad to say), but these did not perform well at the box office. Between 1942 and 1945, the import of all "H" certificate films was banned outright by the Central Office of Information and the British Board of Film Censors. The thinking was that there were horrors enough for the public to cope with in real life. Who would risk being hit by a flying bomb while watching The Boogie Man Will Get You - about an experimental breed of super-soldiers developed to do battle with the Nazis? So when The Curse of Frankenstein opened on May 2 1957 - soon moving to two West End cinemas simultaneously - it seemed like a pot of bright red paint thrown in the face of the film establishment. Immediately, there were debates about the "legitimate" depiction of horror (best seen from out of the corner of the eye) and the "illegitimate" depiction of gore. Hammer was usually associated with the latter. But these debates, too, went right back to the era of the Gothic novel when Mrs Radcliffe's The Mysteries of Udolpho was thought to be a good example of "suggestion" or "obscurity" and MG Lewis's The Monk was thought to be far too graphic for its own good.

The slight feeling of disquiet, the upward cadence in the voice detectable in that letter from the Heritage Lottery people, has taken a very long time to exorcise. Gothic films - and the novels from which they are distantly derived - have until recently been considered guilty pleasures, best experienced late at night when the critical faculties are half asleep. Where Hammer films are concerned, the garish colours, deliberate sensationalism, well-endowed harpies, repetition of sets and locations, and dramas that were thought to have no serious connection with the facts or morals of everyday life, made them, as CA Lejeune famously put it, "among the half- dozen most repulsive films I have encountered". Repulsive is an interesting word to have used in this context, because horror films - like their literary counterparts - have often revelled in being transgressive; in challenging taboos. Think of the Hollywood Murders in the Rue Morgue (1932) in which Dr Mirakle tried to prove the literal truth of Darwin's thesis about the descent of man with help from the over-sexed Erik the ape; or of the censors cutting the sequence where Karloff's creature plays with the little girl by the lakeside, in James Whale's Frankenstein (1931), and throws her into the water thinking she will float like a flower - a cut that actually created the impression that the girl had been molested; or The Tingler (1959), about an attempt by a mad scientist to isolate "the fear virus", which featured the first LSD trip in mainstream cinema. Only no-one noticed because it was a horror movie.

The Gothic has traditionally provided a set of metaphors, of grown-up fairytales, with which to challenge traditional morality and the tyranny of good taste. It has held up a haunted mirror - like the antique one in Ealing's Dead of Night (1945), which reveals how repressed and artificial its owners are - to the true-to-life mainstream of English literature and cinema. As for the authors of the original Gothic novels (such as Ann Radcliffe and Mary Shelley), they did not until surprisingly recently qualify for entry into English literature's all-male county cricket eleven. File under "the popular novel" instead, the sort of material Queenie Leavis - rather than FR Leavis with his "great tradition" - wrote about. And yet, the Brits (often with a Celtic twist) seem to have been particularly good at expressing themselves through nasty stories: the orthodox view is more comfortable with realism in literature and naturalism in visual art.

It was David Pirie's book A Heritage of Horror (1973) that first examined in detail the subtle connections between Gothic cinema and the original Gothic novels of a century and a half before. Some of the key themes of those novels proved equally useful when applied to Hammer films: the fatal man, the beauty of the Medusa, Milton's Satan who has all the best lines, and so on. But research for Tate Britain's exhibition Gothic Nightmares has revealed a parallel story: the many connections that exist between Gothic paintings of the late-18th century and the design or visualisation of horror films. Another heritage of horror.

The clearest example of these connections is Zürich-born Henry Fuseli's painting The Nightmare, first exhibited at the Royal Academy in 1782. In Mary Shelley's Frankenstein (1818) the chilling scene of the creature fulfilling his prophecy to his scientist-creator ("I shall be with you on your wedding night") was almost certainly based on the design of Fuseli's painting:

"Great God!", says Victor Frankenstein when he discovers what has happened to his new wife Elizabeth, "why did I not then expire! Why am I here to relate the destruction of the best hope, and the purest creature of earth. She was there, lifeless and inanimate, thrown across the bed, her head hanging down, and her pale and distorted features half covered by her hair. Every where I turn I see the same figure - her bloodless arms and relaxed form flung by the murderer on its bridal bier. Could I behold this, and live?" The monster meanwhile has a grin on his face: "He seemed to jeer."

A recent scholar has rightly called this scene "straight out of Fuseli's Nightmare". As if to acknowledge the visual debt, the first Hollywood film version, in 1931, based its wedding night sequence - the only one to be directly derived from Shelley's book - on The Nightmare, with Boris Karloff standing at the window and Mae Clarke lying prone on the bridal bier in an exact replica of Fuseli's design. A lobby card of this moment was produced, and the Nightmare pose appeared on some of the posters as well as on the tie-in book jacket. Hollywood art directors from the late 1920s onwards - especially those working on horror films - often turned to northern European visual sources for instant references. Many of these designers were emigrés, and brought their visual culture with them. The art department on each studio project would customarily compile a "bible" of possible visual inspirations, and in the case of Frankenstein, Fuseli's The Nightmare was evidently among them.

But the painting had already, by 1931, been launched into the cinematic bloodstream. In Robert Wiene's German film The Cabinet of Doctor Caligari (1920), the somnambulist Cesare (Conrad Veidt) enters through the painted curtains and hovers over his sleeping victim with a knife, like a black-clad nightmare in human form: the design, like that of a number of German horror films in the Weimar period, revisits Romantic paintings through the prism of expressionism. Three years after Wiene's film, a production drawing by designer Albin Grau, for the climax of FW Murnau's Nosferatu: A Symphony of Terror (1922), the first adaptation of Dracula, seems also to have been directly based on The Nightmare: the vampire, Count Orlock, stares hypnotically through the window at the restless heroine. Many of the visuals created by Grau and Murnau were also derived from the landscape paintings of Caspar David Friedrich (Nosferatu is set in Germany in 1838, two years after Friedrich's death). For the sequence where the vampire finally enters the heroine Ellen's bedroom, though, and she sacrifices herself to him (or does she fulfil her secret desires?), the visualisers turned to Fuseli. In the film, as dawn strikes, the Count - with his leathern ears, bald head and rodent teeth - re-enacts Fuseli's nightmare. And thence to Hollywood. From Whale's Frankenstein onwards, The Nightmare was to be transformed into countless scary variations on the theme of beauty and the beast, a visual heritage eventually bequeathed to Hammer films.

Victorian critics liked to dismiss Fuseli's paintings - and especially The Nightmare - as a case of "Teutonic hobgoblinry". Gothic novels suffered a similar fate. The novels have been seriously reappraised over the past 20 years. Now is a good moment to reappraise their visual counterparts. For, as the novelist Angela Carter used to say, "Today we live in Gothic times." The billboards all round London for a new TV series called Supernatual proclaim Scary Just Got Sexy. Actually it has been sexy for well over 200 years.

· Gothic Nightmares: Fuseli, Blake and the Romantic Imagination is at Tate Britain, London, from February 15 to May 1. Details: 020-7887 8888.