I had some vague inkling of the premise: Alec Guinness and -- it's my understanding that all Ealing Comedies have a description that starts thusly -- his band of villains are undone by a nice old lady while they plot to bump her off. My fractured memory had filled in some gaps: bumping off the old lady was essential for getting their hands on money, so I assumed inheritance, or something similar; and I envisaged some Marple-esque cunning and out-witting.
So: Alex Guinness and his band of villains are stealing a large delivery of cash. They rent rooms in Katie Johnson's boarding house, and pretend to be an amateur string quartet; in fact, while they are 'rehearsing', they're just playing a record in the practice room, and are actually next doors, plotting. Their landlady is essential to their plans because she's their unwitting getaway driver. Guinness plays the mastermind to a tee, calming his increasingly-panicked team and correctly predicting everything that will happen, and the whole job goes smoothly - up to the point where one of them acts foolishly to a chance occurrence, and the cash is spilled in front of their landlady's feet.
Thereafter, she comes to the right conclusion, and they decide they have to kill her - but which of them has the nerve to bump off a kindly old lady, and how? For her part, Johnson isn't attempting to outwit the gang in any way - she's far more forthright than that: they should just give the money back, and hand themselves in, and be ashamed of themselves!
One of the nice things about this is that it's quite short, compared to modern films. This is good because the second half of the film is quite repetitive. It was entertaining, but the humour isn't particularly sophisticated (unsurprising for a film more than fifty years old). But it is quite endearing; the naivety has a charm all of its own.