While the British government has congratulated Trump on his election, the head of the opposition, Labour leader Jeremy Corbyn, said he should "grow up" on the immigration issue and recognize that the U.S. economy depends on migrant workers.
"The treatment of Mexico by the United States, just as much as its absurd and abusive language towards Muslims, is something that has to be challenged and should be challenged," Corbyn, whose wife is Mexican, told the BBC on Sunday.
UKIP, which has only one member of parliament in London, said Farage and Trump spent more than an hour discussing Trump's victory, global politics and Brexit.
A UKIP official has suggested Farage could even be the next ambassador to the United States, but British media reported that May's office rejected the idea of any role for Farage, citing unnamed sources who described him as an "irrelevance".
A day after Trump's election victory, Farage called on the real estate mogul to reverse "loathsome" Barack Obama's policy by making Britain his top priority.
Farage said he had been pleased at Trump's "very positive reaction" to the idea that a bust of former British prime minister Winston Churchill be put back in the Oval Office.
He has also joked about sexual assault allegations against Trump, urging him to "schmooze" May but not touch her. He proposed that in any meetings between the British and American leaders, he could attend to be the "responsible adult to make sure everything is OK."
Farage, who spoke at a Trump rally during the election campaign, had predicted the former reality TV host would tap into the same dissatisfaction among voters that led to Britain deciding on June 23 to leave the European Union.
Trump made repeated references to Brexit during his campaign, saying it had highlighted the desire for change among voters frustrated with traditional politics.