The elderly Mrs Wilberforce leaves her rickety King's Cross house. At the police station, she explains that her friend Amelia's story of a flying saucer invasion was just a dream. The Superintendent thanks her and escorts her out.
A sinister figure follows her home, circling the house before ringing the doorbell. He introduces himself as Professor Marcus, enquiring about the rooms to let. He agrees to move in the next day. She happily agrees to allow him to use the rooms to rehearse his string quintet.
Next day, Marcus introduces the other members of the quintet: Major Courtney, the huge 'One-Round' Lawson and young Harry Robinson. Louis Harvey arrives shortly afterwards and is hurried upstairs by Marcus. Locking the door, Marcus puts on a record for Mrs Wilberforce's benefit and begins explaining his payroll robbery plans. The other gang members, particularly Louis, are uncomfortable about involving the old lady in their plans. They are interrupted by Mrs Wilberforce bringing tea and congratulating them on their playing. After she leaves, they vote on the plan. Marcus wins; Louis reluctantly accepts the decision.
Later, the gang - minus Marcus - are disturbed repeatedly by Mrs Wilberforce, offering teas and coffees and asking for help giving her parrot his medicine. The parrot bites Harry and escapes, causing chaos as each of the gang try to catch him, before finally he is caught by the returning Marcus.
At King's Cross, the gang successfully hold up the payroll van, and transfer the money into a trunk, which is left to be collected as luggage by Mrs Wilberforce. She picks up the trunk under the noses of detectives, who are looking for outgoing parcels. But the watching gang are alarmed when she first returns to the station to pick up her umbrella, then gets into an argument with a barrow boy, causing havoc. Finally, however, she and the trunk return home - with the help of two policemen.
The gang drag the truck upstairs and admire their haul. They repack the money in their instrument cases and prepare to leave. But saying goodbye to Mrs Wilberforce, One-Round gets his cello case stuck in the door. As he struggles to free it, the case opens, spilling money in front of an astonished Mrs Wilberforce.
The gang contemplates escape but, realising the old lady might talk, they return. As they try to find an explanation, Mrs Wilberforce's tea guests - four more old ladies - arrive. One brings a newspaper carrying the story of the robbery. The penny drops. Mrs Wilberforce is appalled, and demands they stay for the tea party.
Afterwards, they try to convince her to be silent, claiming the loss will be met by insurance, inventing misfortunes to justify their actions and, when this fails, warn that she will be implicated and risks jail. When a policeman calls by, she agrees to send him away, but she remains unconvinced, and finally decides the money must be returned.
The gang discuss disposing of her. They draw lots, and the Major loses. The others go down and send Mrs Wilberforce to him. He tells her he is going to the police and climbs through the window and over the roof with the money. The others realise, and Louis climbs after him. The money is recovered and the Major falls to his death.
They draw lots again, but One-Round rebels, and insists Mrs Wilberforce should live. To distract him, Marcus enlists his help disposing of the Major's body over a passing goods train. Harry draws the short straw, but instead of killing her, he steals the case and runs. One-Round returns and finds Mrs Wilberforce asleep. Assuming her dead, he runs after Harry and kills him.
While Marcus and Louis dispose of Harry's body, One-Round overhears them discussing killing him, and pulls Harry's gun on them. But the safety catch is on, and Louis finishes him with a knife. Louis and Marcus fight it out and eventually Louis falls to his death. The professor celebrates, then is struck by a signal and falls himself.
Later, Mrs Wilberforce goes to the police. The Sergeant listens politely, then suggests she keeps the money. Bemused, she goes on her way.
