Labour MP Stella Creasy has called on the prime minister to challenge the US after a UK Muslim family was barred from boarding a flight to Los Angeles.
The family of 11, from Ms Creasy's Walthamstow constituency, had planned a holiday to Disneyland but was stopped at Gatwick Airport on 15 December.
Mohammad Tariq Mahmood said his family was given no reason why US officials had refused to allow them to board.
US officials said travellers were not barred based on religious beliefs.
Downing Street said Prime Minister David Cameron would respond to the issues raised.
Ms Creasy has written to Mr Cameron, urging him to press the US authorities on what she said was "a growing problem" of British Muslims being barred from the US without explanation.
She said she had "hit a brick wall" in her own attempts to get answers from the US embassy.
"A lot of Muslim constituents are now saying to me that they're frightened about flying. They're frightened they're going to lose money, they're frightened they're not going to be able to see relatives."
She told BBC Radio 5 live she was aware of four other UK cases of Muslims being denied entry to the US.
"Nobody knows why these people were stopped. We do know what the common denominator is between them. All of us agree we've absolutely got to be vigilant about tackling terrorism, and we've got to be clear prejudice hasn't got a part to play in that," she added.
Mr Mahmood, who was travelling with his brother and their children, aged eight to 19, had planned to visit their elder brother in southern California and go to the theme parks.
He said UK Border officials told them at the departure lounge that they were not allowed to board the plane, despite them all having authorisation to travel under the US Visa Waiver Programme.
His brother Mahmood Zahid Mahmood, with whom he was travelling, told the BBC: "Just before the final check to get into the lounge we were singled out.
"A man from UK Border Force came and said, 'I'm sorry you can't board this flight. We received a call from Washington DC that we can't allow this family to board the flight.'"
He said he had educated his children "to live in this country peacefully" and had been invited to speak at local schools about Islamophobia.
He told BBC Radio 5 live it had seemed a clear case of discrimination.
He said his children were "traumatised, really upset" after their cancelled trip, saying, "They think they've done something wrong."
"I want an explanation, and what's going to happen next. I would still like to go to America, I would like my kids to fulfil their dreams."
The family said the airline Norwegian had told them they would not be refunded the £9,000 cost of their flights.
They said they were also forced to return everything they had purchased at Gatwick's duty-free shops before being escorted from the airport.
Mahmood Zahid Mahmood also said he had been refused entry to Israel eight years ago. He and another man remained at the airport before returning on a flight two days later. He added that he was not held for eight days, as had previously been reported.
The brothers' other brother, also Muhammad, who runs an auto repair shop in San Bernardino, California, said he could think of no reason why his relatives would represent a threat to the United States and called on his government to explain its actions.
"They can get away with anything by saying national security… and you can not even challenge that," he told the BBC. "There needs to be a reason given."
A US Customs and Border Protection spokesman said: "The religion, faith, or spiritual beliefs of an international traveller are not determining factors about his or her admissibility into the US.
"In order to demonstrate that they are admissible, the applicant must overcome all grounds of inadmissibility."
The spokesman also said there were 60 categories of inadmissibility, including health-related, prior criminal convictions, security reasons and immigration violations.
UK immigration minister James Brokenshire said the government would look into the incident but ultimately the decision was up to the US authorities.
But chairman of the home affairs select committee Keith Vaz said there seemed to be a growing pattern of British citizens being refused entry to the US.
"This is one of our closest allies in the world and the way we treat each other's citizens is extremely important," he said.
"If you imagine if an American citizen was told by a British official they couldn't board a plane, there would be complete uproar in the United States of America."