The documentary also tells how Cameron negotiated with EU leaders Jean-Claude Juncker and Donald Tusk over the concessions he felt he needed to win the referendum - and how the Europeans saw it.
Tusk is particularly open and frank about his discussions with Cameron at the time.
“I told him bluntly, come on David, get real,” Tusk says in the film. “I know that all Prime Ministers are promising to help you, but believe me the truth is that no-one has an appetite for revolution in Europe only because of your stupid referendum. If you try to force us, to hurry us, you will lose everything."
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“And for the first time I saw something close to fear in his eyes. He finally realised what a challenge he was facing.”
On the Brexit referendum, Tusk also reveals that Cameron had initially assured him that there was “no risk of a referendum” as the Conservative’s then-coalition partners, the Liberal Democrats, would block the idea.
After the Conservatives won an outright majority, however, “paradoxically, David Cameron became the real victim of his own victory.”
“Paradoxically, David Cameron became the real victim of his own victory” Donald Tusk
Speaking about the post-Brexit phone call in which Cameron informed Tusk of his resignation plans, Tusk says: “It was like his day of reckoning was coming, reckoning for the biggest mistake in his life.”
The film, “Inside Europe: 10 Years of Turmoil,” was shown to reporters at a special viewing in Brussels on Wednesday and will air on BBC2 at 9pm on Monday.
‘TURNING UP THE HEAT’
In the documentary, former MP Douglas Carswell and Conservative MEP Daniel Hannan reveal how they sought to “turn up the heat” on Cameron.
For the first time on television, former Prime Minister William Hague, former finance minister George Osborne and former deputy Prime Minister Nick Clegg reprise the arguments inside the UK Government that led to the decision which sparked the biggest political crisis in the UK since World War Two.
Osborne warned against a gamble that could be a "disaster for Britain", but Hague thought there was no other option, saying: "This was coming. Either we had to lead that or be the victims of it.”
Cameron’s closest advisers - including his press secretary Gabby Bertin and ambassador to the EU Ivan Rogers - describe the increasingly desperate negotiations, including a last-minute push to get the concessions which would ensure that the then home secretary and now Prime Minister, Theresa May, would back remain.
COMING UNSTUCK
As he runs up against Europe’s leaders, Cameron comes unstuck, says the film. French presidents Nicolas Sarkozy and Francois Hollande, Dutch Prime Minister Mark Rutte, Angela Merkel’s top Europe advisers and other key players recall warning Cameron against picking a fight, and how their vision of the European Union differed from his.
Ultimately, the film, made by UK-based Brook Lapping, says that Cameron “could not deliver enough to win the referendum.”
A BBC spokesman said, “For the first time, Europe’s presidents and prime ministers and their closest advisers take us back behind closed doors, where they battled night after night to keep the European Union together.”
“The series shows leaders such as Nicolas Sarkozy and Donald Tusk not just as politicians, but passionate people trying to defend their project and their countries - with all the contradictions that involved.”
“It opens the lid on the fierce arguments and clashes of personalities between Europe’s leaders, as they struggled with crises which could have torn the union apart,” he added.
A second episode, “Going for Broke”, which is due to air a week later, takes viewers deep inside crucial European councils as the leaders and their ministers try to avert financial disaster.
It is a clash between the cautious Angela Merkel and Sarkozy over how to deal with the near-bankruptcy of Greece. The crisis spreads to threaten the euro itself.