Parade's End follows Tietjens, "the last Tory", a brilliant government statistician from a wealthy Edwardian landowning family married to a flippant, adulterous socialite, Sylvia (Rebecca Hall).
Despite public humiliation, he refuses to divorce her because of what he terms his "parade" - an outmoded code of ethics that is tested by the mass slaughter of World War I, then by Tietjens' growing love for a young suffragette, Valentine (played by Australian newcomer Adelaide Clemens). It's a journey, says Cumberbatch, from romanticism to modernism.
The five hour-long episodes are strikingly filmed by the director, Susanna White (Bleak House, Generation Kill), with nods to such modernist art movements as Vorticism and Cubism. But, by following the same late Edwardian aristocratic caste through World War I and into the 1920s, could Parade's End be fairly dubbed "a thinking person's Downton Abbey"?
"I guess that's a crude label for it," says Cumberbatch. "Not to denigrate what you're saying, but any comparisons are a danger."
However, he later says that Parade's End won't be "some crappy, easily digestible milk-chocolate on a Sunday evening. It's going to be hard work, but it will pay dividends if you stick with it."
Stoppard, who last wrote for the BBC back in 1979, began work on his adaptation four years ago, long before Downton Abbey seduced the world, and what Stoppard calls "the current festival of toffery".
"I was well into the thing before I'd even heard of Downton Abbey and decided not to watch it," he says. "I remembered a friend telling me about going to dinner in a stately home and saying to his host, 'Your butler is very impressive.' The host replied: 'Not really - he buys in his chutney.' I put that into Parade's End, and then somebody said to me that Maggie Smith says something like that in Downton Abbey (it was actually in Julian Fellowes' script for Robert Altman's Gosford Park where Maggie Smith's character dismisses 'bought marmalade - how feeble'). Anyway, I called Julian Fellowes up and he said, 'Oh, just carry on, don't worry about it'. In the end, the things that are similar between these different dramas are much, much less significant than the things that are dissimilar."
Indeed, it's highly unlikely that the subtle moral ambiguities and complex historical metaphors of Parade's End will appeal to the mass audience that imbibes the sudsy Downton Abbey. "It's more ambitious," agrees Stoppard, who spent 15 months on his script.
"It's one of the key modernist novels. This was the period when The Wasteland and Ulysses were published. It was never a huge popular success, but I met four or five people who said, 'Oh, you're doing Parade's End - it's my favourite novel.'
"I absolutely loved the job. Ford was writing at a time when he was interested in experimentation - he puts you inside people's heads and sometimes these people haven't got their heads straight and you have to find your way through the maze of their thoughts. I had a conversation just a few days ago about The Great Gatsby movies and about the novel. I think that Gatsby is a great novel, but how do you put its greatness into a screenplay?"
Stoppard and White had Cumberbatch in mind right from the start. This, however, was before Sherlock made his name international, and with half of Parade's End's $21.6 million budget coming from HBO, the Americans were doubtful.
"To us, he was well known," says Stoppard. "I'd seen Benedict playing roles at the Almeida and other places and I knew he was bloody good, but he wasn't a star by any means. Sherlock actually happened when we were putting it together, which helped a lot."
Stoppard's assiduous, almost fearful wooing of his leading actor began during a visit to the set of War Horse.
"Tom kept on looking at me sideways and he said to me, 'You've had such a wonderful, extraordinary year Benedict'," says Cumberbatch. "It was lovely but there was something slightly odd about the conversation and he confessed to me later that it was agony for him because he wanted to offer me the role there and then.
"The weird thing is I couldn't get past certain things. Christopher is a big man and I was really distracted by that at first. I wanted him to be fatter and rounder; I was thinking of a young Gambon or - dare I say it - Matthew Macfadyen. I've said that before - he's going to punch me next time he sees me.
"I'm this willowy man worn to the bone by doing Frankenstein (at the National Theatre). And then with Sherlock, having to be whippet-thin and eating rice cakes, and running and swimming a lot. I had to put on this fat suit and plumpers in my face [for Parade's End]. I wish we'd gone further with it, but they stopped me going the whole hog because they wanted a pin-up. He's got to be sexually attractive or why would someone as beautiful as Valentine fall for him?"
In the end, he visualised himself into the role by way of the Mayor of London. "I saw him as Boris Johnson to start off with," he says. "A very intelligent but rather oafish buffoon."
Does he now yearn, I wonder, for a change from all these fiercely intelligent men he keeps playing?
"I'd love to do a slacker comedy where I'm just getting stoned," he admits. In fact Parade's End, and the new series of Sherlock, could be the last we see of Cumberbatch in television roles.
Playing the obligatory British baddie in the new Star Trek movie, and co-starring with Brad Pitt in Steve McQueen's latest venture, Twelve Years a Slave has whetted his appetite for a larger canvas.
"I'm playing a really big game now," he says. "I'm going into studios to meet executives and heads of production and asking: 'What have you got on your slate?' and they say, 'This and this and this'. And you know there are five actors ahead of you who have first refusal, so there will be fallow periods now, but I can't afford another five months in the theatre or another big TV gig.
"I think it's time. I don't have any dependants. I'm interested in just playing the game a little bit, because it gives you a lot more choice. It gives you power and if you become indispensable to that machine it gives you a greater variety, which is what I always wanted. My career's always been about longevity - I've never wanted to be an adolescent flash in the pan. "
Who: Benedict Cumberbatch and Sir Tom Stoppard
What: Parade's End, the television adaptation of Ford Madox Ford's novels
Where and when: UKTV from Sunday May 5, 8.30pm
- TimeOut / Independent