Burglars posing as meter readers entered the home of a 31-year-old woman in Harlington Road, Uxbridge, on last Friday on Halloweens day.
The woman saw the man holding a knife to her baby before saying to her, "where is the gold?"
An e-fit of one of the suspects, who pretended to be from a water company, has been released by Scotland Yard.
The man bound the mother's wrists and ankles and put her and her daughter in the bathroom during the raid.
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The mother and daughter were found by neighbours about 50 minutes later, when police were called.
The suspect was wearing a lanyard around his neck and a high-visibility jacket which made the victim believe he was a genuine meter reader, police said.
Emergency services attended the scene and the mother and daughter did not need to go to hospital.
Detective Constable Anji Dawson said: "This incident happened on Halloween at about 17:00 GMT so we believe there may have been many people in the area that may have seen the suspect."