Dozens of viewers are said to have lodged complaints about the sexual content of a scene shown on Saturday in which the Time Lord, played by Matt Smith, was propositioned by his assistant, Amy Pond.
The character, played by Karen Gillan, was seen kissing the doctor and attempting to undress him as he backed up against the side of the Tardis.
At one point Amy, who wears a trademark miniskirt, suggested that they could have a one-night-stand.
She also joked about how long it had been since the 907-year-old Time Lord last had sex, making suggestive innuendoes and provocatively lying down on the bed in front of him.
Some viewers posted complaints on the BBC's message boards pointing out that the episode had been aired in a peak early evening family viewing slot.
One wrote: "We expect this sort of thing from trashy US imports but not a well-respected series like Doctor Who."
Vivienne Pattison of Mediawatch UK, the standards pressure group, said: "I thought it sailed pretty close to the wind."
The Daily Telegraph