Davies began the 1923–24 season slowly, scoring once in his first five appearances although Cardiff scored ten times in the games. From 15 September to 27 October, he embarked on a scoring run, netting in six of the seven matches his side played, which included winning goals in two matches. On 10 November, he scored all of Cardiff's goals in a 4–2 victory over West Bromwich Albion. He went on to finish the campaign as the club's top goalscorer having scored 23 times in the league, a career high tally. However, his campaign was overshadowed by a missed penalty on the final day of the season. In their last game, Cardiff met Birmingham. If they won the game Cardiff would be guaranteed the First Division title. The match was goalless after 70 minutes, when a goal-bound shot from Gill was blocked by the hand of a Birmingham defender resulting in a penalty being given. The club's usual penalty taker Jack Evans had missed recent attempts, while Gill was reluctant to take it. Davies instead stepped in to take the first penalty of his senior career. His teammate Fred Keenor later described the attempt, noting "There is no doubt that the excitement and the knowledge that so much depended on the shot unnerved Len a little. Under ordinary circumstances it would have been a gift goal, but Len Davies muffed the kick and the ball rolled gently to the goalkeeper, who calmly gathered and made an easy clearance." The game eventually ended goalless while their nearest rivals Huddersfield Town won 3–0 and secured the title courtesy of goal average. The difference between the two sides, 0.024 of a goal remains the closest margin of victory ever recorded in the top tier of English football. Davies was said to be inconsolable following the miss.