Since its release two weeks ago, Rivals has swept the nation off its feet, winning critical acclaim and introducing Jilly Cooper, the queen of horsey Rutshire, to a new audience. But for executive producer Dominic Treadwell-Collins, 47, and for Cooper’s literary agent, Felicity Blunt, who is also an executive producer on the Disney+ series, this has been the climax of a slow-burning love.

Blunt, 43, was an “über Jilly fan” from the age of ten. “I was too young to be taking her books out of the library, but I got away with it because I had the large print edition, which had this grey horse going over a set of jumps rather than the bottom [and] hand,” she recalls. “I told my mother it was about horses.” When Blunt became an agent, she made it her “life’s mission” to inherit Cooper as a client when her predecessor, Vivienne Schuster, retired. “I would have killed anybody who got in the way,” she says.

Amid all the attention on the naked tennis and romping in fields, it is easy to forget that Rivals is actually the story of competing TV companies bidding for a franchise. The current series ends halfway through the novel, to avoid galloping through the plot. Inevitably then, amid the buzz around the first series, there are already questions about a second.

Jilly Cooper with her son, Felix Cooper, and literary agent Felicity Blunt in 2015.

Liam Keelan, Disney’s senior vice-president of original content for Europe and Africa, hints that this is likely. “You’d have to be living in a cave not to have come across Rivals,” he says. “Everyone’s talking about it. I’ve seriously never known anything like it. But it’s been on the platform for just over a week, so give us a chance, but hopefully more news to come. Suffice to say, we love the show.”

There may even be a spin-off show born out of Rivals. In the show, TV company Corinium’s biggest hit is Four Men Went to Mow about sexy topless farmers (Aidan Turner, known for his chest-exposing scenes in Poldark, gets to quip: “TV can’t just be men taking their tops off!”).

I ask Treadwell-Collins if they are considering making it. “We would love to!” he replies. “We have a synopsis as the writers had to know what it was, so we’re ready to go.” In an earlier Rivals draft, there was even a scene of it being filmed. “It feels like a very real show,” says Blunt. “I don’t think you’ve seen the last of them.”

Alex Hassell and Emily Atack share one of many intimate moments.

Treadwell-Collins, who made A Very English Scandal, has been hoping to adapt Cooper for years and had been writing to Schuster about it since 2006. He would pitch it in every ideas meeting, but male TV executives would dismiss it, deeming Cooper unfashionable.

When she took over as Cooper’s literary agent, Blunt found Treadwell-Collins’s letters, and told him to write directly to Cooper, who was charmed. “She was like, ‘Yes, take my hand in marriage’,” recalls Blunt. “And I was like, ‘Whoa! whoa!’… But then Dominic came to meet her [at Cooper’s house] and it was love at first sight. Five hours passed, champagne was drunk and by the end it was a gentleman’s handshake that they were going to work together.”

“Everyone’s talking about it. I’ve seriously never known anything like it.”

Cooper hasn’t always enjoyed adaptations of her books. She described the 1993 dramatization of Riders as “dreadful” and thought her leading man Rupert Campbell-Black, the show-jumping cad, was played by Marcus Gilbert as a “total wimp”. But she has called this series “absolutely brilliant. Just heavenly.”

Keelan says it was an easy decision to make Rivals: “It’s Jilly Cooper, national treasure. We knew … people are going to talk about this show, and that it would make people think, ‘Wow, that’s on Disney!’” The company certainly invested in the series, which looks lavish; Treadwell-Collins has described it as “the last show commissioned in the streaming gold rush”.

Claire Rushbrook and Tennant as Lord and Lady Baddingham in Rivals.

On set, Cooper both acted as a muse and sometimes a corrective. “She would occasionally just whisper in my ear, ‘You know, he’d never say that,’” says Elliot Hegarty, 53, the lead director. “It was done with charm and a smile. It was great when Jilly was on set, because everyone was much better behaved, watching their Ps and Qs.”

There is even a cameo for Jilly: while Lizzie, a writer played by Katherine Parkinson, is having lunch with her agent, Cooper is dining at the next table. She smiles as Lizzie reads a salacious extract from her new book.

The sense that Rivals was fun to film pervades the series. The producers imposed a “no arseholes” policy for casting, with due diligence to ensure no actor was going to be difficult, demanding or downright nasty. The cast seem to have embraced the nudity too, which is as much male as it is female, and includes the 40-something actors as much as the youngsters.

In fact, the heart of Rivals is the slow-simmering affair between the equally badly-married Lizzie and Freddie, played by Danny Dyer.

“TV can’t just be men taking their tops off!” Aidan Turner as Declan O’Hara.

Dyer has been a surprise to many viewers, but Treadwell-Collins, who used to produce EastEnders, wanted him from the beginning: “I was writing with Danny in my head. I brought Danny into EastEnders and said to him, when I left, ‘I’m going to come back for you.’ He’s the most brilliant actor.”

One of the show’s challenges was how to tweak the books for a modern audience while staying true to Cooper’s tone. Changes included giving Charles Fairburn, a gay TV executive played by Gary Lamont, a love story, and looking more deeply at a MeToo moment involving junior staffer Daysee Butler (Lara Peake).

“We’re still in Jilly’s world,” insists Blunt, who is married to the actor Stanley Tucci. “She loves the changes; she championed them … We never wanted to lecture people, to tell them what they were meant to think about the Eighties or about today.”

Rosamund Urwin is the media editor at The Sunday Times