In March 1956, Wally and Kitty Hitchens reported strange goings-on in their terraced house on Wycliffe Road in south-west London. Pots and pans would fly across the room, bedsheets would rise off beds, and banging sounds came from the walls and the floor. Some of the noises were so loud, they could be heard by half the street. Later, fires began breaking out in the house and scrawled words would appear across the walls. The police visited, as did clairvoyants and reporters looking for a spooky scoop.

The case was also examined by the paranormal investigator Harold Chibbett, who spent months with the family and made extensive notes. At the centre of these peculiar happenings was the Hitchens’ daughter, Shirley, who was 15 and claimed that the ghost wreaking havoc in their house was called Donald. The newspapers were fascinated by this teenager who was once allegedly seen by her family levitating above her bed.

The Battersea Poltergeist, which re-examines what it calls “Britain’s strangest haunting”, is an investigative series and an audio drama rolled into one. It is presented by the writer and broadcaster Danny Robins, who starts off by telling us: “I don’t believe in ghosts.” Robins goes through Chibbett’s case file, scours newspaper reports and bones up on similar cases such as the Enfield poltergeist of 1977.

He has also assembled a gaggle of experts, among them the parapsychologist Evelyn Hollow and psychology professor and hardened sceptic Ciarán O’Keeffe. The latter puts Robins through a virtual reality test to demonstrate how the imagination can run riot when the mind is under stress. Most remarkably, he talks to Shirley Hitchens, who is now 80 and whose version of events has not wavered. She is extremely convincing.

Amid the present-day pontificating are short dramatised segments, starring Toby Jones and His Dark Materials’ Dafne Keen. These take some getting used to, but prove to be a smart and atmospheric addition, capturing the bewilderment, frustration and terror experienced by the Hitchens family.

The dark heart of this series is also reflected in the wonderful title music, specially created by musicians Nadine Shah and Ben Hillier. This is an enormously intriguing podcast that mercifully avoids trying to scare its listeners with Scooby-Doo-style theatrics. Instead it asks us to empathise with others, open our minds and contemplate matters outside our experience.

There is no shortage of ghostly podcasts, many of them gratuitously hokey and annoying. Lore is not one of these. The series’ focus is on the dark stories and creepy legends of the past, from the tale of Mary Webster, accused of witchcraft and who miraculously survived a hanging, to the “Bunny Man” murders in Fairfax, Virginia. Lore is all about hard fact — whether or not we feel they are true today, all the stories uncovered here were believed at the time.