No stranger to provocative material after starring in four series of the sexually explicit ITV series Secret Diary of a Call Girl, the 29-year-old plays an unhappily married woman who engages in a dangerous affair.
Her character Holly is a secondary school teacher who falls for her teenage pupil, played by Skins star Kaya Scodelario.
A BBC source told The Mirror: "This storyline will get some criticism, but it's been well researched and is similar to real-life events."
Scodelario has previously stated that the lesbian storyline in True Love (previously known as Love Life) is not deliberately sensational, claiming: "It's very hard to get two female actors, put them together in a relationship and not make it about sex.
"[This story] was more about the connection that they share as women [and] the points that they're at in their lives."
The five-part serial was semi-improvised by the actors, and sees Piper re-unite with her Doctor Who co-star David Tennant for the first time since Tennant's final episode as the Doctor in 2010.
True Love airs on BBC One on Sunday, June 17 at 10.25pm.
Watch the trailer for True Love below: