Anybody old enough to remember the sort of spooky stories that showed up as TV movies of the week in the 1970s, especially on ABC (they were often produced by the prolific Dan Curtis), will have some idea of what Nick Willing’s movie is like. “Close Your Eyes” (also known as “Doctor Sleep,” the title of the novel by Madison Smartt Bell on which it’s based, as well as “Hypnotic”) is a throwback to the psychological thrillers with supernatural overtones that were thick on the ground a few decades ago, especially in the wake of “Rosemary’s Baby” and “The Exorcist.” It’s extremely old fashioned and, especially in the final reels, extraordinarily silly, but it’s pulled off with just enough panache to make it a tolerable time-waster–especially if you leave your brain in the lobby (or wait for the DVD release or late-night cable showing).

The hero of the piece is Michael Strother (Goran Visnjic, of “The Deep End”), a psychologist operating under-the-radar in London by limiting himself to cash-only stop-smoking therapy. (He’s in England, along with his wife and young daughter, on a non-worker visa, suffering from the trauma of losing a patient during his previous American practice.) Janet Losey (Shirley Henderson), a policewoman client, blackmails him into using his talent at hypnosis to get through to Heather (Sophie Stuckey), a young girl who escaped from a sadistic serial killer but has remained mute ever since. The investigation that Michael and Janet initiate leads them into a supernatural mystery involving a sixteenth-century heretic with a outre theory about the position of the soul in the brain, a black magic-obsessed English architect who put up eight or ten churches at strategic points throughout the city, and an oddball occultist named Elliot (Paddy Considine) who not only offers the duo the benefit of his weird insights but directs them to an even more knowledgeable source, a cancer-ridden professor named Lebourg (Fiona Shaw). A few twists (and a couple of corpses) later, the pair unravel the plot behind the killings and the reason why Heather is so integral to it, but not before poor Michael has to confront the villain in very uncomfortable circumstances.

“Close Your Eyes” requires an insupportable suspension of disbelief to swallow its increasingly convoluted and absurd scenario. It also concludes with a twist that’s rather cheaply derivative of “Rosemary’s Baby” and “The Omen,” among many older thrillers. Still, it’s been made with a seriousness that’s oddly refreshing during this post-modern era of horror movies that constantly wink at the audience to show how with-it their makers are. Visnjic, Henderson, and Considine–as well as Mirando Otto, who plays Michael’s concerned wife–all approach the material with the same intensity they might devote to one of Shakespeare’s tragedies, as do Shaw and Corin Redgrave (as Henderson’s colleague on the force). Visnjic’s contribution is especially important: he has to carry the picture almost single-handedly, especially in the final reel, where his character is directly threatened by the conspirators; had he shown the slightest indication that he didn’t believe in the material, any chance the picture might have had to hold a viewer’s credulity would have been shattered. (The extravagant plot turns of the last act, along with some tepid special effects, will probably do that anyway, but it’s hardly the actor’s fault.) Henderson, who seems to be showing up in every second British film made nowadays, offers her usual strong work, as do Otto and Considine (whose quirky, vaguely creepy work here is very different here from his turn in “In America”). Shaw’s underplaying is curiously ostentatious, but that’s probably the nature of her role.

Like the cast, writer-director Willing also treats the material with (perhaps undeserved) respect, pacing things well without resorting to cheap scares or shocks and creating a moody, menacing atmosphere. He’s assisted by production designer Don Taylor, art director Mark Kebby ands cinematographer Peter Sova, all of whom do expert work on a low budget, and by Simon Boswell, who contributes a suitably unsettling score.

“Close Your Eyes” won’t rejuvenate a genre that’s probably well past the point of no return, but it has a certain macabre, retrograde fascination that should at least keep you from following the titular injunction while watching it.