Peter Morgan has spent the best part of a decade living with a woman that he’s never met, and hopes he never will. It’s a relationship between two shy people that looks set to result in the most expensive television series ever made; Britain’s leading contemporary screen dramatist chronicling the longest reign in our history.

He’s imagined the private life of Queen Elizabeth II, the most public figure of our age. Morgan has a track record of plays, programmes and films about the real-life mighty brought low by their fatal flaws (President Nixon in Frost/Nixon, Idi Amin in The Last King of Scotland, football manager Brian Clough in The Damned United), which has seen him headily described as a Shakespeare for the TV age.

His previous portrayals of the sovereign, in the film The Queen and The Audience on stage (both starring Helen Mirren), were showered in awards. Now he's doing it again with The Crown, a television drama for US streaming service Netflix.

For him, the attraction of the monarchy is political, not personal. He says he wouldn’t have chosen to base a huge television project on “a woman of limited intelligence, inward-looking, quietly spoken, whose interests are sport and the countryside”.

He sees her as a simple, ordinary person who came to the throne by accident (he calls the abdication of her uncle, Edward VIII, later Duke of Windsor, “a deviation”).

“She would have much preferred the life of a solid English countrywoman, living with her dogs and breeding horses.” Instead, he says, she has spent her long adult life in history’s most amazing ringside seat.

“Through her eyes, you can see the entire second half of the 20th century.” Alongside that, there’s the story of a royal family he sees almost as victims.

“That’s the imprisonment of the institution. And the suffering of the family ripples out from the crown, inflicting profound abuse on people upon whom it’s assumed it only projects luxury. It’s a hideous thing for them,” he says, “but as a drama it’s got everything.”

The result is The Crown, a ten-part series that follows the Queen from her marriage to Philip Mountbatten in 1947 to the resignation of her first Prime Minister, Winston Churchill, in 1955.

Netflix, the American-owned internet streaming service, is releasing it on 4 November. A second series, about the next decade of her reign, is already in production.

Netflix has spent $100 million on it so far and has an option on as many as four more series. It’s sumptuously filmed, in magnificent locations, with a stellar cast – Claire Foy (Anne Boleyn in the BBC’s Wolf Hall) plays the Queen, the former Doctor Who star, Matt Smith, is a dashing and edgy Prince Philip, and the American actor John Lithgow makes a convincing, if rather tall, Winston Churchill.

The re-creation of fading imperial grandeur is immaculate. The 1940s pomp reeks of deference and cigarette smoke. This kind of authenticity is expensive. The then Princess Elizabeth paid for her wedding dress with ration coupons; the screen copy cost £30,000.

It’s gold-plated British television at what it does best but, in this case, television seems to have left the British networks behind.

Morgan had hoped the BBC would do it. But when they wavered, Netflix snatched his arm off. It was mostly luck, he says, but he’s almost pathologically modest, a slight, quietly spoken man with baby-wide eyes that hint of emotions close to the surface.

His pitch to Netflix coincided with a huge expansion of its global subscription service, from 60 countries to more than 190; many of them Commonwealth countries to whom, as he puts it, “the Queen is their grandmother”.

They were looking for a big series that wasn’t US-orientated and they had a $6 billion annual programme budget to burn.

“Normally I’m greeted with a heavy-hearted sigh,” he says, “but I found I’d walked into a room with an idea that dovetailed perfectly with a company’s strategy. For the first time in my life I was in sync with a corporation’s avarice.”

What he’s done is tell the story of a young married woman suddenly pitched onto the throne long before she had expected it to happen. Her father is, rather shockingly, shown coughing up blood at the beginning of the first episode.

He had lung cancer but doctors, Morgan says, colluded to hide the seriousness of it so he could carry on with his duty. He died at 56, “an unnaturally short life for a Windsor – they go on for ever, for God’s sake”.

In an instant, and largely unprepared, he says, the new Queen had to stop being Elizabeth Windsor and start being Elizabeth Regina, “like inviting another person into their marriage”.

Claire Foy, pitch-perfect as the young Queen, brilliantly captures a sense of bewilderment behind an impassive mask of duty.

For Prince Philip – “a more fascinating man than I’d ever imagined” – it was a disaster. “He had banked on another decade or more in the Navy,” Morgan says.

Matt Smith plays him chafing under the restrictions of his new life as a consort; breaking out to become something of a playboy.

“This is very, very, very tricky,” Morgan says. There are hints of liaisons in the series, but no more. “I’m trying to make them human beings but, at the same time, I’m aware that nobody has come forward and identified people with whom Prince Philip did or did not have affairs. I’m not going to be the one to do that.

“I’m not a vindictive person. But I do want to shine a light on human frailty and heroism in equal measure.”

He says the Prince is “a joy” to write. “He tries to contain his own complexity, but it just explodes. It’s uncontainable. His temperament can change on a dime. It makes him unpredictable and dangerous.”

Other characters come across as simply tragic. Princess Margaret’s life, he says, is “a terrific story”. He reckons she was better suited to a conspicuous public role than her sister. “She was much more charismatic; a complete star who, when deprived of the opportunity to express that stardom, turned tragically inwards.”

The Duke of Windsor, too. Commenting on events from resentful exile, he provides a waspishly sharp running commentary that might surprise those who’ve come to think of him as merely shallow and weak.

“Have you read his letters?” Morgan asks, unusually animated. “They’re breathtaking: cruel and dazzling, insightful and mischievous. It’s all there. Great letter writer; lousy king.”

I wonder how he knows what the Queen thinks. She’s spent a lifetime avoiding controversy, bottling her own opinions. “Yes,” he says, “I went into this thinking she was an empty vessel but realised you can tell what she thinks from what she hasn’t said and hasn’t done.

“I suspect there’s a million times she curses under her breath. I imagine her natural sympathies are with the Commonwealth, rather than Europe, and one of the reasons the country was able to contemplate Brexit was because the grandmother of our nation thinks that way.”

Morgan is far from certain he will chronicle the rest of her reign. He wants to see how the first two series go down with Netflix’s 80 million-plus subscribers. “If I’m going to spend the rest of my 50s in this monogamous relationship, I need to know it matters to people.”

He hardly needs the money. Or the fame. He works, he says, for “validation”, but doesn’t explain other than to say it’s more than mere approval. You sense he’s become an admirer of the Queen, not for what she is, but for what she has done: for her stoicism, her sense of duty and her staying power.

She’s still there in her 90s after 13 Prime Ministers, many of whom, as he puts it, “simply chucked in the towel, a confederation of quitters”.

Will the Queen like the series? “Who knows? These are the most written-about, satirised, portrait-painted people in the world. What do they care?” I wonder if he’d like to meet the Queen (he has a CBE already, so a knighthood would be the next step).

He’s horrified at the thought. “I hope never to meet her. I’ve spent so long thinking and writing about the woman it would feel unnatural and uncomfortable. I’d just be embarrassed."

The Crown is available on Netflix from 4th November 2016