It's 1936 Cornwall, and Europe is on the brink of war. But in this small coastal town, such events only play out on the radios of the likes of Janet (MAGGIE SMITH) and Ursula Widdington (JUDI DENCH), two elderly sisters who live along the sea. Nothing much happens in their lives and they seem content that way, but things change when they discover a body lying in the surf following a bad storm the night before.
It turns out to be Andrea Marowski (DANIEL BRUHL), a Polish man with a broken ankle who doesn't speak any English. Due to the language barrier, no one knows where he came from, but after the local physician Dr. Mead (DAVID WARNER) tends to him, Janet and Ursula -- with the aide of their maid Dorcas (MIRIAM MARGOLYES) -- nurse him back to health.
As the weeks pass, the sisters watch over him, with Ursula seemingly having some sort of odd obsession toward him, somewhat motherly yet slightly romantic. Andrea only thinks she's being kind, and surprises everyone when he demonstrates that he's a concert-level violinist. That attracts the attention of Olga Danilof (NATASCHA McELHONE), a new artist in town who also takes a liking to him.
Janet and Ursula are wary of her interest in him, especially since both speak fluent German. As the days continue to pass and Andrea expresses his desire to go to America, everyone begins to question his and Olga's motives, all as Ursula finds herself falling for this man who's many decades younger than she is.