Before she takes on her role as the 13th Doctor Whittaker appears in BBC One's new thriller series, in which she plays a desperate nurse who steals her senior doctor friend's identity after losing her own job for being a whistleblower.
Under the guise of her friend Dr Ally Sutton, nurse Cath Hardacre takes a job at an Edinburgh hospital as a doctor and must attempt to live a dangerous double life without being discovered.
Whittaker said she was drawn to Trust Me because the storyline went in a "completely different direction" from what she first thought.
She also said that she enjoyed that Cath's choices are "morally dubious".
Whittaker, 35, said: "I was sent the script for the first episode and it fascinated me because it went in a completely different direction to how I thought it was going to.
"Particularly at the beginning when she's suspended for whistleblowing and loses her job. It could have gone so many ways, and the fact that she takes on this new identity isn't the way that I thought it would go."
She added: "I love the fact that her choices are quite morally dubious - they certainly aren't black and white.
"She makes decisions that are quite challenging to justify, even though we know her reasons.
"I've never acted in anything medical before, so it felt completely new."
Trust Me also stars Inbetweeners star Blake Harrison as Cath's good-for-nothing ex-partner Karl, The Inspector Lynley Mysteries star Sharon Small as Dr Brigitte McAdams and Paradox's Emun Elliott as Dr Andy Brenner.
Whittaker, who is known for her roles in TV drama series Broadchurch and films including One Day and Attack The Block, made TV history when she was revealed last month to be the first woman to portray the Time Lord in Doctor Who, a role she is taking over from Peter Capaldi.
Trust Me airs on Tuesday at 9pm on BBC One.