A hefty storm is brewing outside a ramshackle office on the isle of Guernsey, carrying with it stories of ghosts and ghouls. Written by James Milton and Paul Morrissey, with localised stories of whispers in tunnels and faces in forests, When Darkness Falls smartly entwines history and folklore. After a shaky start, this is a show that gets smarter and scarier as the night goes on.

Working for the Guernsey Historical Society, John (Will Barton) has stayed late to record a vlog with a writer and paranormal researcher (Alex Phelps). Looking back on the ghost stories that haunt the ancient island, the writer tells John five stories, testing his lack of belief with tales of witches, apparitions and unresolved revenge.

This is the way the first half of the show goes, with the guest recounting these hauntings. Phelps is slick, intense, creepy, but the stories are always a step removed, as if they’re just memorised from a textbook. When Barton’s character adds little bits to the story, sometimes stepping into a character, it feels at odds with the world they’ve created. There’s no heat to it.

But this bafflingly dull beginning is followed by a brilliantly spooky second half, as gradually, elements of the ghost stories start to creep into the room.

Things fall off their perches. The lights go out. John starts hearing things. Once the balance switches, the fear feels close enough to breathe down your neck. Now, the pair hold our attention completely, with Barton’s frumpled nerves complementing Phelps’ taut confidence. Suddenly, the tension is overwhelming. The tales became tangible, and we’re cowering every time the lights get low.

Behind the theatrical tricks and tripped fuses, the script gets stronger too, the story curling in on itself and the loose ends starting to make sense. Although it’s the shocks and screams that make us jump, there’s a vivid sense that the scariest thing on this haunted island isn’t the threat of a ghoulish presence, but the potential of what one human can do to another.

• At Park theatre, London, until 4 September.