“Bill came early one morning into the bedroom. He sat on the side of the bed and he said, I have to tell you something…” is how Hillary Clinton begins her excruciating personal recollection of one of the most scandalous episodes in American history, when her husband, the President, admitted to having an affair with a White House intern.

Telling her side of the story, the former First Lady remains as articulate, wry and composed as she does during the rest of the four-hour documentary series Hillary, charting her extraordinary path through public and private life over the past four decades.

In fact, the only time she visibly cracks is when she recalls their daughter, Chelsea, then 18 years old and in front of the world’s press, taking her traumatised parents by the hand and walking between them to a waiting helicopter on the White House lawn, back in 1998.

With a catch in her voice, Clinton recounts: “Chelsea put herself between us and held both our hands. That was not anything other than her just trying to keep us together. When she did that, I thought, ‘That is just so incredible, so strong and so wise.’”

Such intimate recollections are testament to the rapport created with her subject by the series director Nanette Burstein, who conducted 35 hours of interviews for her documentary, shown by Sky Documentaries and Now TV from 11 June.  

The film premiered at this year’s Sundance Film Festival, where it had some of the audience in tears. In March, Hillary debuted on Hulu in the US. Vanity Fair described the documentary as “enraging and essential”.  

Burstein, Oscar-nominated for her low-budget film On the Ropes, which follows three young boxers and their trainer, says: “Her husband’s infidelity was definitely the most personally challenging part for her, to sit down and discuss openly about how she felt and how she dealt with it. After 30 years, it’s still emotionally fraught.”

More watching through fingers is required when Bill Clinton shares his own memories of this incident, as well as other key moments of their joint history. Of that time, he reflects, “We all bring our baggage to life and sometimes we do things we shouldn’t do. I have no defence. It’s inexcusable what I did.”

Burstein explains: “They’ve never sat down for these kinds of interviews before, so it was an amazing opportunity. It was essential for me that he was involved because he’s been her partner her entire adult life, she has influenced him as he has influenced her. I couldn’t tell her story without his perspective – the good, the bad and the ugly of it.”

Barack Obama is also interviewed, reflecting on his years competing against, and then working with, Hillary Clinton. In the flesh, who is the more charismatic former President? Burstein has clearly learned some diplomatic skills along the way. “They’re an equal measure,” she replies.

Such intimate recollections weren’t initially what the former presidential contender signed up for. Her team had filmed hundreds of hours of behind-the-scenes footage of her 2016 presidential crusade against Donald Trump and a campaign film had been suggested. Once Burstein came on board, however, the parameters naturally widened.

“I wanted to do something far more in-depth about her life,” the director explains. “The arc of the women’s movement and the partisan politics in our country are things I think about constantly, and I realised Hillary’s life was an opportunity to explore both.

“Those same issues are very dear to her heart, and once she felt there was a reason beyond any vanity to tell her story, not just about her legacy but about themes that matter, she became agreeable.”

That momentary loss of composure aside, the four-hour series finds Clinton as articulate and reflective as you’d expect. “She was so unguarded in the recent material, I decided to interweave it with the older footage,” explains Burstein. “I didn’t want people to have to wait until the fourth episode to see that side of her. I wanted them to see it from the very beginning.”

Clinton’s warmth is reciprocated by her clearly devoted aides, as well as her classmates sharing stories of her time at Yale Law School and her campaign surrogates – all proof of a strong band of sisterhood that one would not previously have associated with Hillary Clinton. 

On screen at least, Bill Clinton appears happily sidelined, playing cards with the security team and patiently waiting his turn on stage as his wife’s supporter-in-chief.

Less genial is the documentary’s pantomime villain, Donald Trump, a rival whom all Hillary’s tireless professionalism could not match in the final reckoning. Interestingly, pretty much the only time the cameras stopped rolling was late on election night 2016, when the confusion and scale of her defeat hit home. Nevertheless, her concession speech the following morning – Clinton dry-eyed while so many around her were in tears – is freshly inspirational.

She admits in the film that, once she got in the car, away from the crowds, she, too, collapsed.

Of course, it is this capacity for self-control, as well as her unashamed intelligence, that brings Clinton as many detractors as admirers. The documentary explores the fact that her many critics were more disapproving of her decision to stay in her marriage than they were of her husband’s betrayal.

And the tireless effort she put in as a senator for New York and then Secretary of State (112 countries visited, 1,540,000km travelled) have done nothing to reverse their belief that she had always been in it for something other than public service.

Did Burstein get any nearer to solving the riddle of Hillary Clinton, and what it says about her and her fellow Americans? “When you are a woman trying to push the boundaries, or anyone trying to change culture, you are going to have people who love you and hate you for that reason, because you are trying to shift the way we perceive the world,” she says. ‘Hillary has done that throughout her entire life, particularly once she came into the national spotlight.

“I don’t think the world was quite ready for her personality, so she was a Rorschach test. She was a lightning rod. That’s nothing new, but here you see it in the details of how it was played out for her time and again.”

After so many hours talking together, Burstein remains impressed by Clinton’s preparedness to reflect on her own actions as well as others’ in assessing those challenging times.

“I was surprised by her ability to be self-analytical, self-deprecating and self-­critical, not just putting the blame on others, on the culture, or this or that. She takes some responsibility that a lot of people in her position are not willing to take.” Burstein chuckles. “Of course, we all have blind spots.”

If Clinton gave many valuable hours to the project, so did the director. What are her hopes for how it is received in the UK? “For Hillary, I think she’s been hugely important in our history, so I hope people understand her in a way they never have before.

“Also, in terms of women’s history, how overt the sexism was even not very long ago – I want it to be enlightening, that we still have this unconscious bias against women in positions of leadership. If it’s got better, it’s partly because of people like her, people who are changing or trying to force us to reconceive our ideas of what a leader really is.”

Hillary started on Sky Documentaries and steaming service Now TV on 11 June.​