The family of 11 was stopped from boarding their flight to Los Angeles at London’s Gatwick airport on Tuesday last week by immigration officials.
Mohammad Tariq Mahmood, who was travelling with his brother and nine of their children, said the officials gave no reason for blocking their travel plans.
But he told the Guardian newspaper he believed it was because US officials “think every Muslim poses a threat”.
“Because I have a beard and sometimes wear Islamic dress, I get stopped and asked questions,” Mahmood added in comments to the BBC. “I feel that is part of the deal of flying.”
The family has also been unable to secure a refund for the cost of the flights — around £9,000 (12,000 euros, $13,400).
Mahmood’s local lawmaker in London, Stella Creasy of the main opposition Labour party, has asked Cameron to look into what happened.
Cameron’s Downing Street office confirmed that the prime minister would respond to Creasy’s request.
“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,” Creasy wrote in Wednesday’s Guardian.
“We should do more than shrug our shoulders at secretive American security policies that leave our constituents in such limbo.”
The US embassy in London and Britain’s Home Office did not immediately respond to requests for comment.