Mohammad Tariq Mahmood, who was travelling with his brother and nine of their children, said the US officials gave no explanation for refusing to allow them to board the flight.
"It is because of the attacks on America - they think every Muslim poses a threat," he was quoted as saying by the Guardian.
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A 10 Downing Street spokesperson said that Cameron will investigate the lawmaker's claim and will "respond in due course".
US Department of Homeland Security officials have so far provided no explanation for why the country refused to allow the family of 11 to board the plane even though they had been granted travel authorisation online ahead of their planned December 15 flight.
Mahmood said that the airline told them that they would not be refunded the USD 13,340 cost of their flights.
They were also forced to return everything they bought at the airport's duty-free shops before being escorted from the airport.
"I have never been more embarrassed in my life. I work here, I have a business here. But we were alienated," Mahmood told 'The Guardian'.
Creasy said she is concerned about increasing numbers of British Muslims being stopped from entering the US with no apparent reason.
Writing in the newspaper, she said she had "hit a brick wall" with getting an explanation from American authorities and so has asked Cameron to intervene.
She said: "The vacuum created by a refusal to provide any context for these decisions is fuelling resentment and debate.
"Online and offline discussions reverberate with the growing fear that UK Muslims are being 'trumped' - that widespread condemnation of Donald Trump's call for no Muslim to be allowed into America contrasts with what is going on in practice."
All British citizens fall under the "Visa Waiver" programme, which authorises travel to the US for up to 90 days without a visa.
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