I should tell you right off that I suspect I would need to watch this again to really evaluate how well or poorly the story holds together. But I am not inclined to, because although the first 2/3rds are fascinating, the ending turns in a direction that I thought did not live up to or support the foundation built by the bulk of the movie.
The movie begins with a wonderful credits sequence by Saul Bass, with a hand ripping away black paper, revealing white paper [with black credits] underneath. It helps establish the brittle and edgy tone of the film.
Then we start the story proper. Here's the deal: Ann Lake has just arrived in Britain, and her daughter goes missing after her first day at a new school. Also involved is a guy we assume at first to be her husband, but find out about 30 minutes in that he's her BROTHER. Ann asks around the school for a while, when they finally bring the police in, in the form of Laurence Olivier as Superintendent Newhouse. It becomes apparent that no one other than Ann can be proven to have seen the child, and people start to wonder if the little girl exists at all, or if Ann is just bonkers. Persuasive evidence that she is begins to be revealed.
It can quickly be seen that there's some thrilling technique on display here. Throughout the movie, there are riveting LONG shots that follow a character for a great time and often great distance. There are also strange and expressive sequences that underline what is happening in the story. In one, as Ann is heading upstairs to look for her child, she walks upward through a virtual river of children coming downstairs. Their laughing and screaming dominates the soundtrack. There are similarly strange sequences later, such as when Ann has to search through a doll shop, once again surrounded by hundreds of tiny human-like figures, and again later, when she has to change her clothes in a room full of caged monkeys!
The strangeness also extends to the characters. There is a lot of mileage gotten out of the culture clash between the new American arrivals and the Brits. Notice that in almost every scene the British people INSIST on speaking first, usually telling the Americans something [how much they hate making junket, about children's dreams and nightmares, etc.] before they let the other person speak. or even ask what the other person is doing there in the first place. And then there's the fact that, for quite some time, EVERYONE seems to be plumb bonkers. None of this seemed to really go anywhere, but it did help keep the first half of the movie floating on an air of suspicion and sustaining an off-kilter tone that keeps things on edge.
Among the nutcases are Noel Coward as Ann's landlord, who is as bizarre as the day is long, and comes on to her incredibly heavily, without paying any attention to her refusals ["Perhaps you should sample the wine before sending it back to the cellar," he says]. He ends up being sent home with some police officers, whom he kindly asks to cane him! There is also the dotty Miss Ford, grand dame of the school, who greets the news that Ann's child may be missing with a cheerful "Oh, have they lost one? How careless!"
It's all going very well, and the way it's put together is flawless, until toward the end it takes a turn toward slasher movie territory, and this can't help but leave one [i.e. me] disappointed. It's just got such a deliciously off-center buildup that an ending that explains what's going on can only come off as conventional. It may simply be that we've seen similar scenes in the intervening years in films such as Single White Female. It also seems that the possibilities raised during the first 3/4th of the film were much more interesting than the reality offered at the end.
But the beginning was put together so well that I am willing to believe that perhaps there's something about the resolution that I'm missing.