The Twelfth Doctor (under the pseudonym Malcolm Tucker) destroys British politics from the inside. Iconic Doctor Who favourites such as the TARDIS, the sonic screwdriver and K-9 don't appear presumably due to the more adult-oriented nature of the programme.
Additional Characters Edit
The show also features several familiar faces from Doctor Who, although many with different names.
Seb as Ollie.
Walsh (The UNIT lady from The Zygon Invasion) as Nicola Murray.
Douglas, the incompetent scientist from Pyramid at the End of the World, is Dan Miller.
The Master is in disguise as Julius Nicholson.
Also there’s a bunch of literally who’s that played a minor roll and show up occasionally.
The Controller from Bad Wolf is in it.
One of the Monks.
Van Statten’s Guard/Sycorax/UNIT Soldier/who cares?
Pangol from The Leisure Hive.
Some kid from The Mind Robber.
An extra from Robots of Death and The Face of Evil.
Probably more, but I’ve had enough searching IMDB.