LONDON (Reuters) - Allegations from the United States that British spy agency GCHQ snooped on Donald Trump during his election campaign are "arrant nonsense", the deputy head of the U.S. National Security Agency (NSA) said in an interview on Saturday.

President Trump has stood by unproven claims that the Obama administration tapped his phones during the 2016 White House race. On Thursday his spokesman cited a media report that Britain's GCHQ was behind the surveillance.

Richard Ledgett, deputy director of the NSA, told BBC News the idea that Britain had a hand in spying on Trump was "just crazy".

"It belies a complete lack of understanding of how the relationship works between the intel community agencies, it completely ignores the political reality of 'would the UK government agree to do that?'", Ledgett said.

There would be no advantage for Britain's government in spying on Trump, given the potential cost, he said.

"It would be epically stupid," said Ledgett, who is due to retire shortly.

Current and former NSA officials have described an acrimonious relationship between intelligence agencies and the Trump administration.

Trump, who became president in January, tweeted earlier this month that his Democratic predecessor Barack Obama had wiretapped him during the late stages of the 2016 campaign. The Republican president offered no evidence for the allegation, which an Obama spokesman said was "simply false".

Fox News analyst Andrew Napolitano on Tuesday accused the Government Communications Headquarters (GCHQ) - the British equivalent of the NSA - of having helped Obama to spy on Trump.

White House spokesman Sean Spicer quoted Napolitano's comments on Thursday.

GCHQ said the claims it spied on Trump were "utterly ridiculous" and should be ignored, in a rare public statement.

On Friday, Trump said questions on this should be asked of Fox News, not him.

(Reporting by Andy Bruce; Editing by Dale Hudson)