Davenport began his car racing career in 2011, competing in the Ginetta Challenge.

In 2014 Davenport moved to the Ginetta GT4 Supercup on the TOCA BTCC support package.

Davenport spent the next two seasons in the British GT driving for Tolman Motorsport.

For the 2017 season, Davenport was signed by Motorbase Performance to compete in the British Touring Car Championship.

Davenport is participating in the 2020 season of the Britcar Endurance Championship in a Ligier JS2 R for Reflex Racing with Marcus Vivian.