I can see some folks wanting to run a Game with no Time Lord in it, the appeal is an obvious one - there will be no one player who can 'Lord' it over the rest of the group!
One of the problems with such an approach, is getting the Characters around.
Here are a list of Temporal Devices, that may (or may not) come in useful . . . .
BUT I would't give them a Broken Tardis - thats a "destroy the universe if you get something wrong" plot device LoL!
I would go for one of the many different Time Machines that have been seen in Doctor Who stories.
The Ancient Horologe
The Ancient Horologe was a very delicate instrument linked to time itself that measured the passage of time across different dimensions. Crafted like an ornate clock by the master chrono-smiths from the older worlds, it was given to Lord and Lady Tubbs as a wedding gift from the Doctor and had pride of place in the Clock Room of Croxton Hall. It was damaged when a thief dropped it in a scuffle with Lord Tubbs. As a result, a fracture in time was created displacing those nearest to it into a different kind of time. (Very fragile, and probably better suited to being the focus of a Campaign/Scenario - rather than a games main Travel Device).
Chula Warships were spaceships that could travel in time. Chula Warships were fully equipped with tractor beams and Nanogenes. These warships could also turn invisible, to avoid detection. (This would be my favourite option, the group could find a crashed Chula ship and repair it).
Circle of Mirrors
The Circle of Mirrors was a time travel device created by the alternate UNIT of Donna's World, by harnessing the the power of the Doctor's salvaged TARDIS. It allowed Donna Noble to see the invisible Time beetle on her back and allowed her to go back in time and turn left. (Not brilliant, but might be useful as a one-off device in a game).
A DARDIS was a dimensionally transcendental space-time vessel created by the Daleks so that they could chase the Doctor through time and space. One of these craft enabled the Doctor's companions Ian Chesterton and Barbara Wright to return home. The Doctor set the ship for self-destruction after it had transported them to 1965 London. (What if it DIDN'T self destruct, maybe the explosion just buried it - for the group to find many MANY years later).
The Machine was one of the earliest forms of TARDIS. It was created in the time of Omega, and The Other used it to get Patience off of ancient Gallifrey. (A more basic Time Capsule, and so would be easier for the PC's to pilot - with less chance of them screwing up too!)
The Time Cabinet was an early experimental time machine from the 51st century which used zygma beams. (Unfortunately, zygma beams can be deadly in any great quantities).
The Time Controller was a method by which one faction of Daleks in the Imperial-Renegade Dalek Civil War used to control their method of time travel. Physically, the Time Controller was a globe which appeared to only be used by a Human controller. (This, though limited - would be great in a heavily Dalek orientated campaign - with the Daleks and the Time Travellers having the ability to track each-other using their Time Controllers).
The Time Converter was a handheld device possessed by Sarah Jane Smith which allowed the detection, opening and closing of time fissures in areas where the Web of Time remained thin. Fearing that she might use it to alter her timeline as she had recently, Sarah Jane destroyed it. (If you were to use one of these, that would be great - it would give the campaign an almost 'Sliders' feel to it).
Time Rings are small time travel devices created by the Time Lords. The first Time Rings were worn on one's wrist, and later ones were worn on one's finger. (I would favour this, especially if the group have to travel continually to one specific place and time - sent there by some higher power).
The Time Tree
The Time Tree was a tree which enabled time travel. It was possible to time travel simply by plucking its seeds (which grew into other time trees). It had orange coloured leaves. They had an appetite for heavy metals. However the method of time travel was not exact, one seed could take someone back a 1000 years, another seed could go back 10,000. (Not the most reliable method, good for a one-off scenario though).
Tribophysical Waveform Macro-Kinetic Extrapolator
The Tribophysical waveform macro-kinetic extrapolator was a long, flat device which, when ridden like a surfboard massive wraps the user in a protective bubble enabling them to ride the energy from a vast explosion. (TECHNICALLY this could be used for Time Travel SHOULD the explosion be temporal in nature).
A vortex manipulator was a form of basic time travel used by the Time Agency of the 51st century. The vortex manipulator allowed the user to travel through time using the Time Vortex. Under normal circumstances, it can allow travel of a distance of nearly 200,000 years. Following modifications with a sonic screwdriver, it could allow travel from the End of the Universe to the 21st century. The Doctor considered it very primitive compared to a TARDIS, describing his TARDIS as a "sports car" to Jack Harkness's "space hopper". Presumably the vortex manipulator created some sort of shield to protect an Agent from the side effects of an unprotected journey through the vortex. This did not, however, prevent some considerable discomfort for the user, as shown by the Doctor, Jack and Martha's responses upon arriving in London. (Another good one, some great plot devices to be used here).
More thoughts tomorrow - Drew