Alan Mckim, a barrister, returns home early to prepare his vintage car Genevieve, a 1904 Darracq, for the next morning's London to Brighton car rally. Alan's wife Wendy, who would prefer to go to a party, complains about his obsession with the car and the rally. Later, Alan offers to forgo the rally, even though his family has been participating in it for twenty-five years, but Wendy relents when she finds the hat Alan has bought her for the occasion.
The next morning Alan and Wendy meet Ambrose and his latest girlfriend Rosalind at Hyde Park for the start of the rally. Shortly after starting, Alan and Wendy argue again, but soon make up. Later, Genevieve's steering breaks down, delaying Alan and Wendy's arrival in Brighton by several hours. It is only then that Alan admits that, after their first argument, he had cancelled their hotel reservation; they will have to find alternative accommodation.
After finding a second-rate hotel, they join Ambrose and Rosalind at the club party. Dancing with Wendy, Ambrose confides that he has always wanted to combine the annual race with a sexual conquest, but something always goes wrong. Ambrose asks Wendy if she has ever told Alan of the time that they came down to Brighton together, before Ambrose introduced her to Alan. Rosalind becomes quite drunk and her comments about Wendy and Ambrose's relationship make Alan jealous. Rosalind joins the band on stage and plays a trumpet solo, to everyone's amazement, then passes out, ruining Ambrose's hopes for a night of passion.
Back at the hotel, Alan and Wendy argue about her early relationship with Ambrose and he opts to work on the car rather than go to bed. Ambrose, with nothing to do except exercise Rosalind's dog Susie, joins him in the garage. The two argue over Wendy and in anger Alan bets that Genevieve would beat Ambrose's 1904 Spyder in a race back to London. The next morning Wendy is furious to discover that Alan has bet £100, practically their entire savings, but then realises that she was responsible for Alan's jealousy for failing to tell him that there was never anything between Ambrose and herself.
They go ahead with the race. Alan and Wendy are soon stopped for speeding, but Wendy manages to talk them out of it. When Genevieve's fan belt breaks, Alan accepts a tow to the garage, even though Wendy considers this cheating. Ambrose and Rosalind catch up. Ambrose complains that being towed is cheating, but Rosalind points out that they were pushed themselves when the Spyder had trouble starting. Ambrose and Rosalind continue the race while Genevieve's fan belt is replaced. Even then, the car won't go; Alan realises that Ambrose has sabotaged Genevieve. Ambrose and Alan meet near a pub seven miles from London and have an angry exchange, which is broken up by the police.
The two call off the bet, but then decide to race to Westminster Bridge, with Genevieve as the prize. They race neck and neck until an old gentleman accosts Alan and Wendy and relates how much he used to love his old Darracq, in which he proposed to his wife nearly 50 years earlier. Although the Spyder overtakes them, Alan doesn't have the heart to interrupt the man and invites him and his wife to drive the car the following day. Wendy is moved by Alan's kindness, realising that the old man's affection for the car matches Alan's own, and that of his father and grandfather, who had previously owned and raced Genevieve. She makes him promise to keep the car, even if it costs them the £100. Although far in the lead, Ambrose's car wheels get caught in tramlines and Alan and Wendy reach the bridge first. Ambrose and Rosalind soon join them and the four embrace.
