The film begins in a BBC studio with the 100th edition of "In Town Tonight". Flotsam and Jetsom open with a "topical number". Then there is an interview with a distinguished actor, which dissolves into a performance of one of his famous melodramas about a wicked moneylender etc.

It is England in the 1830s. London's dockside is teeming with ships and sailors who have made their fortune in foreign lands. Sweeney Todd, a Fleet Street barber, awaits the arrival of men whose first port of call is for a good, close shave. For most it will be the last time they are seen alive. Using a specially designed barber's chair, Sweeney Todd despatches his victims to the cellar below, where he robs them of their new found fortunes and chops their remains into small pieces. Meanwhile, Mrs Lovett is enjoying a roaring trade for her popular penny meat pies.