Stella Creasy, a member of the opposition Labor Party, says US officials gave no explanation for refusing to allow her constituents to board a flight from Gatwick Airport on Dec. 15.
She said this is part of a larger pattern affecting British Muslims, and that a lack of information from US officials is sparking resentment among Muslims who feel discriminated against.
The issue is sensitive in part because US presidential contender Donald Trump has called for a temporary ban on Muslims visiting the US.
Creasy's office told The Associated Press Wednesday that she had written to Cameron seeking his intervention. She complained that US officials who kept the family from boarding provided no information and complained she had hit "a brick wall" seeking information about the case.
Creasy told the prime minister there is "growing fear" among British Muslims that aspects of Trump's plans are coming into practice even though they have been widely condemned.
She warned that some Muslims believe the public condemnation of Trump's position "contrasts with what is going on in practice."
Cameron's office said he would look into the matter. He had earlier characterized Trump's policy as "divisive and wrong."
US Embassy officials declined immediate comment Wednesday, the Associated Press reported.