Craig Oliver also claims Boris Johnson may have been about to back remain instead
Former British Prime Minister David Cameron was furious with Theresa May's absence during the EU referendum campaign and felt she had left him to "fight alone", according to an insider account.
Craig Oliver, the former prime minister's director of communications, claimed Mr Cameron asked her 13 times to "come off the fence" but was "stonewalled".
Mrs May, then the UK home secretary, took many weeks to declare whether she was for leave or remain, after Mr Cameron allowed Cabinet ministers to campaign either way.
But after choosing Mr Cameron's remain side - in what was seen as a coup for him - she was barely visible during the campaign.
She gave just one lukewarm speech in late April, in which she criticised "those that say the sky will fall in if we vote to leave."
In his book 'Unleashing Demons: The Inside Story of Brexit', serialised in the UK's Mail on Sunday, Mr Oliver describes her behaviour as like a "submarine" and "sphinx-like", and suggested her silence was calculated to benefit from a Leave win.
Mrs May only nailed her colours to the mast, he claimed, after Mr Cameron became so "wound up" during a phone call that he hung up on her.
Mr Oliver writes: "From her point of view, it's a smart strategy, trying to demonstrate she is her own person, allowing her to have her cake and eat it, but it doesn't seem fair on DC [Cameron] who has treated her well...she is on the right side making clear she is 'in' but not looking overly enthusiastic. It's making life uncomfortable for us."
He adds: "Amid the murder and betrayal of the campaign, one figure stayed very still at the centre of it all - Theresa May. Now she is the last one standing."
The book also alleges Boris Johnson - whose support for leave was one of the most dramatic moments of the campaign - sent David Cameron a text 24 hours before his announcement suggesting he had become "depressed" about his decision, and may back remain instead.
Mr Cameron's former close friend Michael Gove, who he is reported to have stopped speaking to since the referendum, was said to have assured the prime minister of his support during a Christmas gathering of the two families.
Another book, also serialised today by the UK Sunday Times political editor Tim Shipman, quotes unnamed sources close to Downing Street, claiming Mrs May failed to support a plan to curb EU immigration during the campaign.
Mr Cameron had wanted to announce controls of immigration days before the public voted, in what he hoped would be a game-changer.
But sources claim Mrs May and her now chancellor Philip Hammond failed to support the plan - citing Angela Merkel's opposition to it - leading Mr Cameron to brand both of them "lily-livered".
In the end, he dropped plans for the "emergency brake" on immigration at the last minute and announced curbs to migrants' access to welfare in the UK - which was much criticised by the leave side.
The claims prompted an angry response from a Downing Street source, who said it was "utterly untrue to suggest that Theresa did not want immigration controls".