Tappin, who fought extradition for two years, said he had looked to British Prime Minister David Cameron to protect his interests but "he failed to do so," The Daily Telegraph reported.
"I have no rights," Tappin said at Heathrow police station, where he was handed over to U.S. authorities.
Tappin, 65, is accused of conspiring to sell components for Iranian missiles. If convicted in a U.S. court, he could face a possible 35 years in jail. He denies the charges.
Cameron Wednesday said the government would conduct a ''proper, sober and thoughtful'' review of its extradition policies, adding that extradition treaties "show respect to each other's judicial processes and make sure that people who are accused of crimes are tried for those crimes."
The Home Office was accused of a cover-up because it did not publish evidence behind a controversial review of extradition laws.
Conservative lawmaker Dominic Raab said Wednesday the public may think there "was something to hide" and called on the Home Office to release the information it gave to retired Judge Scott Baker for review, the Telegraph said.
Baker's review last year determined the treaty wasn't biased and didn't need to be reformed.
2014: The Year in Music [PHOTOS]