The stunning actress, 36, is currently starring in Agatha Christie’s three-part series Ordeal by Innocence opposite Bill Nighy, 68, on BBC1.
Alice, daughter of Waking the Dead star Trevor Eve, 66, bared her body in the steamy scenes from the flick opposite Star Wars actor Harrison Ford.
Ordeal by Innocence peaked with 5.2million viewers when it launched on Sunday night, and continues this weekend.
It was originally meant to air at Christmas but bosses were forced to re-shoot scenes after actor Ed Westwick, 30, pulled out as a result of sexual harassment allegations.
Alice’s steamy scenes aren’t the first time her body has made a stir.
An underwear scene starring Alice from 2013’s Star Trek Into The Darkness caused outrage after fans branded it “unnecessary”.
The film’s writer Damon Lindelof was later forced to issue an apology.
He said: “I copped to the fact that we should have done a better job of not being gratuitous in our representation of a barely clothed actress.”
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