Image copyright PA Image caption Iain Duncan Smith called for "humility" in the wake of the EU vote

Claims Theresa May "badly let down" David Cameron over the EU referendum campaign have been dismissed by former Conservative leader Iain Duncan Smith.

Mr Cameron's former director of communications Sir Craig Oliver said in a book that Mrs May was regarded by some as "an enemy agent".

But Mr Duncan Smith urged Remain campaigners to "get behind Theresa May instead of carping".

Sir Craig said the book was an attempt to explain "what went wrong".

In his book, Sir Craig claimed that Mrs May failed to back the Remain campaign 13 times and he also said Boris Johnson believed the Leave campaign would be "crushed".

'Pin the blame'

Former Work and Pensions Secretary Mr Duncan Smith said in a statement: "In the past, a knight of the realm who had failed in battle and lost would have quit the field and retired in humility to better understand their own failings.

"How surprising then to find that far from that, Sir Craig Oliver, one of the leading lights of Remain, has decided to instead try to pin the blame for his failure on others, particularly the new prime minister.

"Craig Oliver's is one of a growing number of foolish attempts by ex-government Remainers who lost to shift responsibility for their failure.

"The grown-up thing for them to do, instead of carping, is to show some humility and get behind Theresa May as she seeks to get back control of migration with the EU as we leave."

Mr Duncan Smith said far from failing to support Mr Cameron in his bid to get a better deal with the EU, Mrs May made her backing for tougher migration controls quite clear.

In response, Sir Craig said Mr Duncan Smith appeared to have got the "wrong end of the stick".

"I have not made the specific allegations he claims," he said. "The book is a sincere and honest attempt to explain what went wrong; and I take full responsibility for the mistakes made by the campaign."

Image caption Sir Craig Oliver (left) was Downing Street director of communications for five years

Sir Craig's book, titled Unleashing Demons: The Inside Story Of Brexit, is being serialised in the Mail on Sunday. Neither Downing Street nor Foreign Secretary Mr Johnson have responded.

Speaking on the Murnaghan programme on Sky News, Conservative Party chairman Sir Patrick McLoughlin said he did not think it was true "at all" that Mrs May had let down Mr Cameron.

"Theresa May during the referendum campaign made her position very clear, " he said. "This is a book that has been written after the event. You have got to have certain spicy things in a book to sell it.

"I don't blame Craig for doing that. At the time, Theresa was very much part of the Remain campaign."

However, former Northern Ireland secretary Theresa Villiers, a pro-Leave campaigner, said there were times when she "did wonder" if Mrs May was listening to both sides.

She told BBC One's Sunday Politics: "Her major speech of the referendum campaign expressed real concerns about the possibility of Turkey joining the EU. It also said that the sky is not going to fall in if we leave."

'Off the fence'

In the book, Sir Craig said Mr Cameron briefly considered staying on as prime minister, despite losing the referendum.

However, he said he decided against it, saying he feared remaining in Downing Street would have left him "being prepared for the slaughterhouse".

Mr Cameron resigned as prime minister the day after the result and was replaced by Mrs May.

Sir Craig said Mrs May only came "off the fence" in favour of Remain after Mr Cameron became "visibly wound up" and gave her a dressing down over the telephone.

Sir Craig's book suggests Mr Cameron was left uncertain over whether Mrs May favoured staying in the European Union.

He said Mrs May was referred to dismissively by aides as "submarine May" during the campaign.

The then home secretary's "sphinx-like approach" became difficult, he added in the book, as the press were questioning which way she would jump.

Sir Craig said matters finally came to a head after a newspaper warned Mr Cameron faced "last-minute opposition" from Mrs May to his deal for EU reform.