On a break from rehearsals for John Dove’s production of Arthur Miller’s play The Price, which opens the post-Christmas season at Edinburgh’s Royal Lyceum Theatre, Gillett was re-acquainting himself with a city he knew well. He was married at

St Mary’s Cathedral, and his now former wife, the actress Sara Stewart, familiar to TV viewers as the dysfunctional mum in Sugar Rush, grew up here.

Gillett was walking in Charlotte Square, trying to keep both his balance and some kind of aesthetic dignity as he trod pigeon-toed on the icy surface below him, when he felt someone tap him on the shoulder. He stopped, only to be confronted by an Australian chap standing with a somewhat starstruck young lady.

“’Scuse me, mate,” said the man. “Weren’t you in The House Of Eliott? It’s my fiancee’s favourite bloody programme.”

Such, then, is the power of the immaculately turned-out Sunday-evening television drama that ran for three series between 1991 and 1994. Set in the sort of between-the-wars milieu already familiar to its creators Eileen Atkins and Jean Marsh from their work on Upstairs Downstairs, The House Of Eliott charted the fortunes of two sisters left destitute following the death of their brute of a father. Forced to sell the family home to pay their inherited debts, their only means of survival is their passion for dressmaking. With the financial help of photographer Jack Maddox, played by Gillett, a cottage industry grows into a leading international couture house in a rag-trade to riches scenario.

As the ultimate English gentleman adventurer with a social conscience, Maddox, meanwhile, turns film-maker, investigative journalist and, eventually, politician. He also marries, loses, then gets back together with elder sibling Bea, played by Greenock-born Stella Gonet.

Along the way, and all in the course of on-set duty, you understand, Gillett also got to snog genuine posh girl Louise Lombard, who, as uber-bobbed younger sister Evie, wafted through every scene as if astride a vintage catwalk.

All of which is a far cry from The Price, in which Gillett plays Walter, a successful surgeon estranged from his brother Victor who returns home after their father’s death to sell off the furniture. On the face

of things, Walter may wear the trappings of his single-minded fortune well – but, as becomes clear, to get where he is he’s lost a whole lot more than a brother.

“I think Miller is a bit more left-wing than most Americans are happy with,” Gillett observes of the 1968 play while sprawled out on a sofa in the Lyceum rehearsal room, “and Walter represents a good, go-getting, positive seeker of the American dream. That just happens to not be where Miller’s heart lies, so his brother is imbued with something more resembling a socialist ethic.

“Walter is more about saying that if something’s not working, then get out, make lots of money and save yourself. He’s not an unpleasant guy, but he’s had to use a few elbows to get what he wants. But that’s what you have to do in the capitalist system. There’s a lot of politics in this play, but it’s an emotional play. It’s about families, love and letting yourself down by letting your family down, and how important your roots are.

“Walter had a breakdown three years before the start of the play. His marriage is tits-up, he’s not close to his sons. The only person he’s got is his brother, whom he hasn’t seen for at least 16 years. He was so busy succeeding that he didn’t realise what this absence was until he had a breakdown.

“That sometimes happens to people. They’re too busy to think about emotions. Now he has to, and see what happened after he deserted his family. Miller takes hold of people’s hearts. It looks like it’s going to be pretty ordinary – then you’ve got people tearing each other and themselves apart.”

This is the sort of heavy stuff actors relish. How, though, does someone so matinee-idol chipper as Gillett tap into such material? Without a hint of self-pity, he points to his separation from Stewart two years ago.

“I’ve been through a kind of trauma, so there’s been a painful time, especially coming up here, which I always associate with my ex-wife. Walter’s recently separated as well, so he’s very raw, and I suppose at this point in my life I’m quite raw as well about all those things. So it’s a little painful, but I suspect if you’re going to honour the play it would always be painful. It’s quite heartfelt, and that’s not hard for me to access right now.”

Born in Yemen before his family returned to England, Gillett first stumbled on acting by chance. He dabbled at university, and condemns his youthful self as “a total loser” who didn’t have a clue about much. To give him a kick in the pants, a girlfriend sent off for a drama-school prospectus. Gillett auditioned, and got in. Things happened quickly with a season at the Royal Exchange in Manchester. Other high-profile work followed, including a Royal National Theatre tour of Michael Frayn’s Noises Off, and work on plays by Pinter, Shakespeare and Coward with Peter Hall. Somewhere in the midst of all this, Gillett was cast in the Broadway transfer of Stephen Daldry’s seismic reinvention of An Inspector Calls.

“I got to New York after buying a Hoover,” Gillett says of his audition. “Hoover made this massive cock-up, where if you bought a Hoover they gave you two free tickets to New York. While I was there, I heard they were auditioning, and went for it. It was something I always wanted to do, but it was like a cul-de-sac. You turn up, do it, and it doesn’t matter where it is, theatre’s theatre, and you can’t see the audience much, and once the novelty of Broadway wears off, it becomes just another show.”

Nevertheless, Gillett won a Best Newcomer award – but while the show was a huge hit, America never embraced him career-wise (unlike his former colleague in The House Of Eliott, Louise Lombard, who went on to appear in CSI).

Gillett returned to Britain, and now finds himself playing an American in The Price. Beyond that, he goes back to playing posh in a new production of The Little Hut, a farce by Andre Roussin adapted in the 1950s by Nancy Mitford.

“It’s quite a nice contrast,” Gillett says, “going from Arthur Miller to Nancy Mitford. It’s like The House Of Eliott all over again.”

The Price is at the Royal Lyceum Theatre, Edinburgh, January 15-February 13.