Sarah Parish is not an actress who blends with the background. Heads turn to watch her progress - a loose, athletic slink - through a restaurant in London’s Mayfair. It’s not a celebrity thing. It’s a presence thing. Immaculate in pencil skirt and silk shirt, Parish radiates the kind of grown-up glamour, a vermouth-and-olives sophistication, that sends waiters diving for chairs.

Maybe it’s the sheen of success - she’s currently starring alongside James Nesbitt in ITV1’s Monroe, where her character, heart surgeon Jenny Bremner, is struggling to come to terms with life as a working mother. But this week the Yeovil-born actress trades Leeds for Hollywood glamour when she joins Kevin Costner in Hatfields & McCoys, a US miniseries that recently garnered 16 Emmy nominations (the same number as Downton Abbey) and won five (second only to Homeland and Game of Thrones).

Either way, the “Call me madam” aura is quickly dispelled by a manner both confident and confiding. “I don’t usually look like this,” offers Parish, 44, best known on this side of the Atlantic as the star of Mistresses and Blackpool. “I just faked it up because I’ve been on This Morning. I’m much more a jeans-and-wellies type of girl.”

Nor - by any stretch - could her part in Hatfields & McCoys be described as a glamour role. She plays Levicy Hatfield, the long-suffering wife of Devil Anse Hatfield (Costner), whose down-and-dirty feud with the neighbouring McCoy family is a keystone of American social history.

“It’s a true story. I’d never heard of it, but it’s hugely famous in America. The feud started during the Civil War, but came to a head with a falling-out over a pig. Which could really only happen in the Appalachian mountains in the late 19th century. Then it just escalated and became this all-out massacre.:

“Levicy was a real tough cookie, a great character to play. She had 13 children, which was normal for the period, and it wasn’t a great time for women. Their husbands had gone off to war and they would be left on a farmstead with all the work to do and all the children to feed. Wives weren’t ‘heard’, particularly, but they were the rock of the family.”

Parish originally read for the part of Sally, matriarch of the McCoys. “When they rang and said I’d been offered a part, but it was playing opposite Kevin Costner, I nearly crashed the car.”

A four-month shoot in the Romanian mountains with a US crew gave Parish ample opportunity to observe the American work ethic. “It was cold and miserable a lot of the time, we were working long hours and it was dirty and grubby, but there’s an energy when you work with Americans that I love.”

“I’m not saying it’s better or worse, but they take their work incredibly seriously. There’s always a stress around it. And you either come up to the mark or you go under.”

“There’s no going out and sitting in the bar till four in the morning. You go to bed at ten o’clock. Then you get up and go to the gym and do a day’s work. You look the best you can and you are the best you can be. American actors exude this confidence and optimism and I just think, ‘Good on you!’ I think sometimes in England we are too ready to put ourselves down. It’s not ‘cool’ to work hard, whereas in America it’s really cool to work hard and it’s really cool to succeed. It’s an honest way of being and I really like that.”

“Having said that,” says Parish, with a luxurious stretch, “I came home and went straight into Monroe, which is a very English job and it was quite nice, between takes, to sit down with my polystyrene cup of tea and my custard cream and have a gossip. It’s two very different ways of working and it’s lovely to do both.”

Parish and her actor husband James Murray (they met on hairdressing drama Cutting It) have a young daughter, Nell, and she is grateful for the relative freedom their lifestyle affords. “I think it’s incredible how professional women like [my Monroe character] Jenny manage to keep all those plates spinning. Being an actor is so lovely sometimes, because you can take off as much time as you want. I didn’t want to work all summer because Nell was just about to start school, so I didn’t. Jim’s work is predominantly in the States and my work is predominantly here.”

“We’re not quite at that luxurious stage where we can afford to take childcare in turns - we do have somebody to come in to help with Nell as well - but so far we haven’t had a big chunk of time where I’m in England and he’s not.”

“We’re very countrified as a family now. We found this fantastic little house in Hampshire. We have chickens and ducks and a dog and an acre of land. Nell loves it because she has fields to play in and ponies to ride. And I love waking up every day in the fresh air.”

It is de rigueur for British actors to profess nervous horror of the “LA lifestyle” (at least until they get the “call”, when you don’t see them for dust). For all her new-found bucolic bliss, Parish is not of their number. If the stateside popularity of Hatfields & McCoys brings in offers from Hollywood she will be delighted. “I’ve done a couple of films over there [The Wedding Date and The Holiday] and I’ve always had a good time. The ‘pilot season’ is great fun because it’s basically ‘Soho moves to LA’. You see all your mates, get a nice tan, hopefully get a job… what’s not to like?”

Lazing by a pool, however, is not Parish’s style. A recent sojourn in Vancouver (“Jim was working and I was being his set-bitch”) introduced her to barre-tone exercise – “a brilliant way to change your body-shape” - and she recently set up her own exercise studio in London.

The “try anything once” principle is also apparent in her acting career, which has taken her from Yeovil Youth Theatre through sitcom and medical drama to Shakespeare (she was a cracking Beatrice to Damian Lewis’s Benedick in a 2005 retelling of Much Ado About Nothing).

“If I ruled TV I would mix things up a bit,” she says. “I get tired of seeing the same faces in the same type of drama. I think that sometimes we’re a little safe over here in our casting.”

“America is better at giving people chances to expand their repertoire. Like when Quentin Tarantino thought, ‘I’m going to put John Travolta in Pulp Fiction’ and everyone thought, ‘What? John Travolta from Grease? You’re going to put him in one of your art-house films?’ And - bingo! - it worked. That’s where you find brilliance.”

The very notion of brilliance triggers a physical reaction that has nothing to do with welly boots and chickens. The disciplined, barre-toned body is taut with expectation.

Hatfields & McCoys starts tonight at 9pm on Channel 5