This is the story behind the case:
In August 1977, Peggy Hodgson called police to her council home in Enfield, England, after two of her four children claimed that furniture was moving, and knocking sounds were heard on walls. A police constable said that she saw a chair slide on the floor and "was convinced that nobody there had touched it." Later claims included allegedly demonic voices, loud noises, thrown rocks and toys, overturned chairs, and children levitating. These claims attracted considerable press attention, and the story was covered in British newspapers such as the Daily Mail and Daily Mirror, until reports of these incidents came to an end in 1979. (Source: Wikipedia)
The case has been widely discredited as a hoax--similar to the Amityville horror alluded to in the beginning of the film. The main reason for this is that Janet Hodgson admitted to and was caught on tape fabricating some of the events. However, she claims to have invented only 2 per cent of them because she was afraid that investigators would not believe her. She maintains to this day that the majority of the supernatural events did happen. To read a recent interview with her, please click here.
The psychic investigators Ed and Lorraine Warren, convincingly played by Patrick Wilson and Vera Farmiga, have also been dismissed as benign, but delusional in their search for ghosts and demons. But others such as Maurice Grosse of the British Society for Psychical Research steadfastly maintained the authenticity of the events. (Grosse, a character in The Conjuring 2, died in 2006.)
You be the judge after listening to the actual voice recordings at the time!