According to the Thirteenth Doctor, positrons produced by the Tsuranga's particle accelerator interacted with the fuel materials to produce heat, which produced thrust. (TV: The Tsuranga Conundrum [+]Chris Chibnall, Doctor Who series 11 (BBC One, 2018).)
The Rocket ZA685 operated on a chemical fuel, of which there was barely enough for a return journey from Earth to the Moon, however the Moon continued to have fuel storage into the 2080s. (TV: The Seeds of Death [+]Brian Hayles, Doctor Who season 6 (BBC1, 1969).)
The fuel rods in the Doctor's TARDIS were meant to be constantly submerged in fuel. If the fuel drained, the rods would cool and start to warp. (TV: Journey to the Centre of the TARDIS [+]Steve Thompson, Doctor Who series 7 (BBC One, 2013).)
When it was making its approach to Kyoto to drop the Big Momma atomic bomb, the Sky Jack was damaged and began losing fuel, making the plane unable to reach its target. (TV: Sky Jacks [+]Andy Diggle and Eddie Robson, Doctor Who (2012) (IDW Publishing, 2013).)