The one-off 90-minute drama for BBC Four will follow the couple's private and public relationship, played out against the backdrop of their ill-fated appearance in a 1983 revival of Noel Coward's stage play, Private Lives. In Private Lives they played a divorced couple who rekindle their romance, but they had already divorced for the second time when they put on the production on Broadway.
The trailer shows a scene in rehearsals where Burton asks Taylor: "What have you taken?!"
In another scene in a dressing room he says: "We're addicts Elizabeth, you and I," to which she replies: "Love is not a drug."
Taylor and Burton's relationship began when they worked on the big-budget movie Cleopatra and the couple married in 1964.
Their first 10-year marriage ended in divorce in 1974 but they tied the knot once more the following year in a remote Botswana village. Their reunion lasted just five months.
Burton, an alcoholic, died aged 58 in 1984, a year after the production of Private Lives.
In the trailer, Helena Bonham Carter looks strikingly like Taylor in a number of outfits from iconic photographs of the Hollywood star.
Helena's partner Tim Burton revealed last month that her preparation to play Elizabeth Taylor had got on his nerves.
He told Vogue magazine: "She's been Elizabeth Taylor, very annoyingly, for several months now. She has been reading lots of things, making notes, studying. She's like a scholar. You would think she was writing a biography."
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