We are a year on from the first, Suez-era series of Morgan's drama. It's now 1957 and Prime Minister Harold Macmillan is telling voters they've never had it so good which, for the immigrant families running vice in Soho - and the Metropolitan Police officers paid to turn a blind eye - was undeniably true.
"Series one was very much about post-war austerity," says Morgan. "Series two is really about us preparing ourselves for the 60s, and a time when London was feeling a sense of glamour. But the counterpoint to that was a dark, seedy underworld, a lot of it related to these migrant families."
The day-to-day reality for West filming all these nightclub scenes involved smoking a lot of fake fags ("those honeydew cigarettes - we tried every brand and they're all awful") and sipping flat cola and cold tea as if it was hard liquor. But the Old Etonian actor did get to imbibe on a delicious storyline, as Hector finds himself wooed by the BBC's brash new commercial rival, ITV, and slips out of his depth in the company of his "friends" in the underworld.
"It was an actor's dream, my story arc," enthuses West. "In episode one, I start as this celebrity on top of the world and within two or three episodes, he descends into the pits of shame and ignominy. You very rarely get a part like that and it was a real challenge. I don't know what viewers will think - I don't tend to think about that - but just in terms of a character arc, it was a wonderful season for me."
Morgan agrees. "In the first series, Dominic is completely charming, strong and is in many ways unbreakable.
"Series two is very much about this man being taken on a downward spiral, and I was really inspired by Dominic and where he can go as an actor."
Exactly where West can go as an actor was forcefully demonstrated by his Bafta-winning performance as serial killer Fred West in Appropriate Adult - a bit of a one-off, he remarks, and he was glad to get back to The Hour.
"I got a huge sense, coming back for the second season, of familiarity," he says. "It saves you so much time and effort, particularly between actors, because we had a rapport. We knew each other's foibles. That's the nice thing about doing the second season - you get stuff done more quickly."
But hadn't the actor turned his back on television after his epic five seasons playing Detective Jimmy McNulty in The Wire?
"I was very reluctant to do any more episodic television," he had told me on an earlier visit to the now-de-commissioned town hall in north London where The Hour is filmed.
"What I like about acting is that you do something intensely for a finite amount of time and then you move on, and episodic television just goes on and on and on. In America, the contracts are such that you feel that you're being co-opted into a vast corporation and that they own your arse for a very long time, and you don't get that sense, thank God, here."
In fact, West turned down a meaty role in the epic HBO fantasy Game of Thrones because it meant shooting for six months in Iceland, and being away from his family in London. He lives in Shepherds Bush with his wife, Anglo-Irish aristocrat Catherine FitzGerald, and their children, Dora, Senan and Francis (West has an older, teenage daughter, Martha, from a relationship with Polly Astor, a grand-daughter of Nancy Astor).
West was born in 1969 into an Irish Catholic family from Sheffield, where his father owned a plastics factory.
The relatively short shooting schedule for The Hour also meant West has the freedom to pursue his eclectic, post-McNulty career, with projects ranging from Disney's US$250m ($300m) Edgar Rice Burroughs movie adaptation, John Carter to the low-budget Irish short, The Girl with the Mechanical Maiden. And he has just opened to rave reviews in the acclaimed Royal Court Theatre production of Jerusalem writer Jez Butterworth's new play, The River.
In the meantime, West has been optioned for more series of The Hour, Morgan telling me that she hopes to set any next series in 1960 or 61. "Well, I've got 10 years of school fees to get through," she says with a laugh. "No, I really would love it to grow."
And grow it most certainly has. The second series feels more confident and less clumsy, with no noticeably (to my ears, at least) anachronistic language, the first series having been peppered with such modern expressions as "Note to self", "Farting about" and "You just don't get it", and "bottled it" - not recorded in the Oxford English Dictionary until 1979.
On the evidence of the opening episode of the second series, The Hour seems to have truly found its feet. Ben Whishaw's character, the hot-headed Freddie Lyon, returns from America with a beard and a surprise for the object of his unrequited love, Romola Garai's producer, Bel Rowley (the character based on innovative 1950s producer Grace Wyndham Goldie, and yet arguably the least plausible of the leading characters). And a newcomer has been drafted in to replace Anton Lesser's Clarence Fendley, the head of news who was revealed to have been a Soviet mole.
Peter Capaldi, best known for playing the foul-mouthed Malcolm Tucker in The Thick of It gives a far more low-key (but strangely just as menacing) performance as the new BBC executive, Mr Brown.
"I came very late to The Thick of It and I'm very glad because I think I would have been incredibly intimidated if I'd seen how brilliant his performance was in that," says Morgan, who wrote the part specifically for the Scottish actor. Capaldi's character brings a new sense of jeopardy to the newsroom, clashing repeatedly with Hector.
Another difference with the first series is the way in which Morgan wrote while episodes were being filmed. It also allowed Morgan to have digs at West, for his poor timekeeping and ever-expanding stomach.
"First of all because I'm so late, she put in 'Hector is always late'," says West. "Lots of great speeches about being late how rude that is and unprofessional. And then it was how fat he was. And we did have incredibly good caterers on the shoot and because it was incredibly long hours you look forward to lunch. I put on about two stone."
Who: Dominic West
What: The Hour, season two
Where and when: SoHo, Mondays 8.30pm
- TimeOut / Independent
