Fervent cyclist Murdoch Troon (Stanley Baxter) is ran off the road by impatient tycoon Charles Chingford (James Robertson Justice). Tracing Chingford back to his home he meets and falls in love with Chingford's daughter, car-mad Clare (Julie Christie). Egged on by his fellow lodger and racy car saleman Freddy Fox (Leslie Phillips), Murdoch decides to invest in 'The Fast Lady', a vintage Red Label Bentley to try to woo Clare. First, though, he has to learn to drive. His instructor, a veteran whose nerves are going, is terrified as Murdoch's obstinate nature comes to the fore and they narrowly avoid disasters with lorries and old ladies. Worse still, an incident in the main street involves none other than Clare's short-tempered father.