Gareth Roberts' Only Human features the Ninth Doctor, Rose and Captain Jack as played by Christopher Eccleston, Billie Piper and John Barrowman respectively. It's set after "Empty Child" and "The Doctor Dances" (two of my favourite episodes from Season 1 of New Doctor Who), but before "Boom Town".
The Doctor, Rose and Captain Jack are about to head off to Kegron Pluva, a planet with a very unusual ecosystem and seasonal cycles, when a device in the TARDIS indicates that there is a temporal disturbance somewhere. Explaining that it's caused by a "dirty rip engine" (an extremely primitive and dangerous form of time-travel) that's causing the disturbance, the Doctor pilots the TARDIS to Bromley. They arrive to discover a Neanderthal Man, twenty-eight thousand years after his race became extinct. The only way to discover just what Das is doing in the 21st century, is for the Doctor and Rose to take a trip back to the primeval dawn of humanity. They can't take Das with them as he is unable to travel in Time: the primitive "dirty rip engine" has warped Das' cells so that a second trip through Time would tear him apart. The Doctor therefore deputises Jack as Das' "babysitter", telling him that he has a month to teach Das about life on 21st century Earth, whilst he and Rose investigate.
Arriving back in the past, they find a mysterious group of humans from the distant future (beyond the 21st century) who are now living in the distant past. They also discover some hideous monsters who are trying to escape from behind a "Grey Door", and Rose is told she's going to have to marry a caveman, one of a group of humans who are keen to kill off the local Neanderthal population. Rose and the Doctor find themselves desperately trying to learn the truth behind the Osterberg Experiment before the monstrous Hy-Bractors can escape to change humanity's history forever.
I enjoyed the presence of the outrageous Captain Jack, who, on being asked by the Doctor to provide a distraction, promptly strips naked and streaks through Bromley, in this novel. He's part of the reason I enjoyed "The Empty Child" and "The Doctor Dances" so much - he had some of the best lines in that two-parter (they'll be turning up in later "Doctor Who Quote of the Week" posts).
Only Human is also available from Amazon.com.