A Type 70 TARDIS was used by the renegade Time Lord and artist known as the Clocksmith, who was also a member of the Doom Coalition. As part of the Doom Coalition‘s plan, he travelled to the world of the Solvers with trinkets to amuse them so then he could disassemble their queen and enslave the Solvers to do his bidding. The Clocksmith used his TARDIS to transport them to Earth.
The Eighth Doctor identified it as a Type 70 by the sound alone it created as it materialised whilst he was a prisoner of Thomas Cromwell in 1538. The Clocksmith learnt from a previous visit, which took place a little further ahead, that the Doctor was killed trying to escape from Cromwell and came back through time to make sure it happened, so the Doctor could not interfere. But he didn't know that Cromwell, after seeing the Doctor's TARDIS leave, made Brother Octavian falsify the records making it appear the Doctor was executed trying to escape and giving him the means to ensure the Doctor did not interfere with his plans as he slipped back in time to ensure the events took place. Octavian, who was in fact the Eight, watched the Clocksmith arrive in that point of time and stowed away inside his TARDIS.
The Clocksmith used his TARDIS to pick up metal that had once come from Syra, the first world destroyed by the Sonomancer, and the first major casualty caused by the Doom Coalition. He fashioned the metal into the Doomsday Chronometer, but it was broken up by Resolva, who had returned to save her people from the Clocksmith, and he was forced to travel throughout Earth's history trying to find the pieces. His TARDIS assumed the shape of a wall.
The Doctor tracked the Clocksmith's TARDIS, noting how the Clocksmith had travelled in and around Earth's history. When the Clocksmith was killed and the Doomsday Chronometer was assembled, the Doctor and River Song stole the TARDIS and used its fast return switch to return to the Tower of London. River was impressed by the newer TARDIS, though she wasn't familiar with the term "Type 70" until the Doctor explained it was a later model of his own TARDIS. (AUDIO: The Doomsday Chronometer)