THERE'S a good chance Tony Curran's face has been beamed into your living room in recent weeks. The Glasgow-born actor is currently a ubiquitous figure on television screens across Scotland – and around the world for that matter – thanks to Netflix movie Outlaw King.

Curran plays Angus Og Macdonald, Lord of Islay, in the David Mackenzie-directed biopic of Robert the Bruce. The character is a loyal supporter as Bruce is crowned King of Scots in 1306, there at his side through enforced exile and fierce combat alike.

When we speak, it is early November and Curran is in Los Angeles where he has been shooting Deadwood, the much-anticipated movie based on HBO's acclaimed western drama series starring Ian McShane.

He begins by telling a story about "driving like a wild man" while wearing a nightgown. It transpires this wasn't for a film or TV role, but rather that his daughter Beau, five, had dressed up as Little Red Riding Hood for Hallowe'en.

Curran was the Big Bad Wolf and his wife Mai completed the line-up as the ill-fated Grandma. He had to hotfoot it from the Deadwood set to join them.

A chuckle of delight crackles down the line. "Sadly, I missed the Trick or Treating but we had a laugh when I got home," he says. "It's not every day you put on a nightgown. That was good fun. One minute I'm a frontier character [in Deadwood] and the next I'm dressed up as the Big Bad Wolf."

LA-based Curran, 48, has twice jetted across the pond in the past month for red carpet duty. The first was to attend the Scottish premiere of Outlaw King in Edinburgh, followed by the Bafta Scotland Awards in Glasgow a fortnight later where he was nominated for best film actor.

When he speaks, there is a tiny hint of a Californian twang but within minutes that has evaporated as Curran's Glaswegian accent comes to the fore.

Apparently, I'm not the only one to have noticed this morphing dialect. Later he will tell me: "A lot of my friends in Glasgow say: 'You have been in California too long, you don't sound as Glaswegian as you used to …' But over here you do have to slow down a little bit."

Curran is a man much in demand. As well as Deadwood, he recently shot the new series of crime drama Ray Donovan starring Liev Schreiber. This autumn he received a Bafta Scotland nomination for the Netflix thriller Calibre alongside Jack Lowden (who scooped the gong) and Martin McCann.

But it is Outlaw King we're here to talk about. It is a topic on which Curran has plenty to say, the passion palpable in his voice as he speaks.

"The story of Robert the Bruce has never, in my opinion, really been told before," he says. "You had William Wallace, of course, with Braveheart. Bruce is taking up where Wallace left off. It is important because he is arguably one of the most iconic kings Scotland has ever had."

Shooting the film, says Curran, was an incredible experience. "The Highlands – along with many other places in Scotland – always have a special place in my heart. I travelled up there as a kid and went hiking Munros."

He reels off a list of his favourite spots. "Glencoe, Rannoch Moor, Ullapool, Skye, Lewis, Arran and Mull. I have always been enchanted by them. They are so beautiful, rugged and timeless.

"There is a little melancholy that is attached to the history of Scotland and that land. You would be sitting there on your horse, dressed in the medieval garb, and look around at the geography in front of you – the land – and it was awe-inspiring."

He enjoyed working with Mackenzie and Hollywood star Chris Pine who is the film's eponymous hero. The star-studded line-up includes Aaron Taylor-Johnson as James Douglas, Florence Pugh in the role as Bruce's second wife Elizabeth de Burgh and Billy Howle playing Edward II.

The £85million film culminates in Bruce's landmark victory over the English army at the 1307 Battle of Loudoun Hill. The cast, including 400 extras, converged on Mugdock Country Park near Milngavie to film the bloody, mud-splattered scenes.

"A great word to describe it is brutal," says Curran. "I chatted with Billy Howle, Aaron Taylor-Johnson and Chris Pine about this and it wasn't like when a lot of actors describe something and say: 'Oh, it was tough'. We were like: 'Well, what did you expect?'

"We knew it was going to be challenging. We did a lot of fight rehearsals, sword training – my character Angus wields an axe – as well as horse training and some stunts.

"As an actor you can only imagine the battles throughout history and how these men fought. How difficult and terrifying it must have been to be running at someone with an axe or a sword knowing this could be your last moments on the planet."

Curran can attest to the effort poured into what viewers see on screen. "David wanted to make a film of historical significance. Of course, there is going to be poetic licence – there is that in every film – but the historical nature of Outlaw King was as accurate as was humanly possible.

"With the battle sequences, when you were rehearsing, there would be 15 stuntmen but then [during filming] suddenly there are 200 people around you. You have horses rearing up. You need to be prepared for things that you don't rehearse for. You have to stay on your toes."

The raw emotion of filming those scenes, he says, is visible in the final cut. "There is no doubt about it," he says. "There are some characters who die in the end and I felt quite moved. The whole experience of shooting that for two weeks was physically and mentally exhausting."

Curran was born in Robroyston in north-east Glasgow and grew up in King's Park on the south side of the city, only a stone's throw from Hampden. He is the youngest of four children. His late father Eddie was a taxi driver and his mother Mary, who turns 85 this month, worked for British Telecom.

He talks proudly about his mother joining him on the red carpet for Outlaw King last month. "She is a very beautiful woman," says Curran. "My mum is strong, funny and doesn't take any nonsense. I have got a lot to thank her for the way I turned out.

"My dad drove taxis all over Glasgow. I was in my late twenties when he passed away. He was a bit of a character and would drive me to school in his hackney cab. He was a good man. I miss him."

Curran studied at the Royal Scottish Academy of Music and Drama in Glasgow (now the Royal Conservatoire of Scotland) before cutting his teeth in a raft of theatre, television and film parts. Early roles included The Tales of Para Handy, Rab C Nesbitt and Taggart.

There was stint on hit TV series This Life in the mid-1990s alongside Daniela Nardini and Andrew Lincoln. Curran went on to win critical acclaim for his role opposite Kate Dickie and Martin Compston in the 2006 film Red Road, directed by Andrea Arnold.

In more recent years, Curran has graced our screens in motorcycle club drama Sons of Anarchy, sci-fi western Defiance and Matt Palmer's gripping thriller Calibre, set in the Scottish Highlands.

While he opted for a Brooklyn accent playing a New York police officer in Ray Donovan (so authentic that even Liev Schreiber did a double take when he heard Curran was in fact Scottish), the actor is thrilled to be using his Glaswegian brogue on Deadwood.

"When I put myself on tape [for the audition] I did a deep south accent – I won't mention the vernacular because it is very colourful – and the casting director Libby Goldstein said: 'Tony, that's great, but can you use your own accent?' I was like: 'My own accent? What do you mean?'

"Of course, there were plenty of Scots around at that time along the frontier, so it totally made sense. So, I get to play my own accent which is very refreshing. It was nice to do that."

Outlaw King is available to watch on Netflix now