In 1938 at a boarding house in London numerous residents live out their lives. There is Mr Josser, newly retired from his firm after 42 years, but not looking forward to it, and whose daughter Doris looks to move out to a flat of her own, much to her mother's anger. There is Mr Puddy, a fat man who cooks fish most days, and Connie Coke, a faded actress who is being chased for the rent by landlady Mrs Vizzard, a widow woman. And there is Mrs Boon and her son Percy, who fantasies about gangster movies and girls and who is involved in respraying stolen cars at the garage he works at. And of course there is the mysterious Mr Squales who arrives looking for a room. Observing it all is the final resident at 10 Dulcimer Street boarding house, Dr Otto Hapfer, a German immigrant who writes letters to a correspondent in Germany and who unbeknownst to the others is a Nazi spy.
Mrs Vizzard is astonished to discover that her new lodger Mr Squales is the clairvoyant Professor Corlito. But she is outraged when she learns that Connie Coke is in jail and decides to take the chance to evict her from her flat - which proves easier said than done. Doris Josser is still determined to move into a flat of her own, despite her mother's objections, so pal Doreen Smyth decides to speak on her behalf at a meeting at Jossers flat that develops into a wider audience than they intended. This is partly due to Percy, who has become attracted to Doris after meeting her at the cinema, despite having a girlfriend in Edith Watson, who works there. But after learning that Edith is married from Jack Rufus, and disgruntled at Jack for cutting the money for the resprays, Percy decides to break from both and go it alone. But his attempt to go into the car theft business goes tragically wrong.
The newspapers are full of reports of Edith Watson's body found near a stolen car, with Percy in a panic over the night's events. However, upon reading that police are looking for two men seen with the girl the night she died, he decides to try his chances and seek out Doris Josser at her new flat. Doris is finding flat sharing with Doreen harder than she thought, but it is at one of Doreen's many parties that she meets medical student Bill Davenport. With Doris moved out, the Jossers take in a new lodger as Fred goes back to working at his old firm debt collecting against his wife's advice. But while Fred later falls dangerously ill with pleurisy, the lodger is not what he seems.
Percy Boon is charged with Edith Watson's murder. With the residents reeling, Mrs Josser decides to break the news to Mrs Vizzard herself rather than find out in the newspaper, but faces a bigger shock when she discovers that Mrs Vizzard is engaged to Henry Squales. But Squales is keeping all options open and when he receives a letter from Mrs Jan Byl for a new seance he sees a money making opportunity, not realizing that his intended is not so blind in love as he thinks she is. Doris and Doreen quarrel over Bill, but her decision to walk out of the flat has an unexpected outcome. Meanwhile Mrs Boon collapses and is hospitalized. When Fred Josser visits her in hospital, she asks him to use her dead husband's life insurance to pay for Percy's defence, only to leave Fred conflicted when he learns that the money will not be enough for a barrister.
Britain is at war with Germany, but the residents of 10 Dulcimer Street are more concerned by the trial of Percy Boon for the murder of Edith Watson. Everything seems to be going well until the defence decide to put Percy in the witness box. Doris is worried when Bill is granted a commission to go into the Royal Army Medical Corps, while Mr Squales seeks to better his image and get more money out of his intended Kitty Vizzard. He receives a letter from the wealthy Mrs Jan Byl to conduct a seance at her country house, but his journey there does not go entirely to plan as he becomes haunted again by disturbing visions.
Percy is found guilty and is sentenced to hang. Henry Knockall decides to go door knocking to raise a petition against the sentence and ropes Mr Josser into helping him, but the later march in the street proves fatal for someone. Percy finds himself haunted by nightmares of Edith Watson, while Mrs Josser is distraught when son Ted is called up into the army. But Doris' offer to move in with Ted's wife Cynthia while he is away ends up angering her mother, as does her announcement that she and Bill are not to have a church wedding. Meanwhile Mr Squales continues to pursue his wealthy benefactor Mrs Jan Byl in seances, but Mrs Vizzard is becoming increasingly suspicious of his activities.
The Jossers decide to use Henry's money to look for a country cottage. Mr Squales faces an ultimatum when Kitty Vizzard tells him she has set a date for their wedding within the week, but a letter from Mrs Jan Byl sees him flee during the night. However, he underestimates the wrath of a woman scorned. Meanwhile as the war rages on it gets a little too close to call for the residents of 10 Dulcimer Street, while there is tragedy for one family.