In fact, he's all three. And for this week only he has a fourth label: erstwhile local hero enjoying a sentimental return to Nottingham. Neville has flown in from his home in Toronto to give three performances of Krapp's Last Tape, part of the 50th-anniversary season at Nottingham Playhouse, the theatre which he ran, with great success and satisfaction, from 1963 to 1968.
In jeans and black X-Files jacket, Neville looks a good deal younger than his 73 years. It's an age at which he might be forgiven for shirking risky challenges, such as having to hold an 800- strong audience single- handed as Krapp, the elderly Beckett hero reflecting on a life measured out in tape spools. So why do it? "It's partly because I wanted to be involved in the anniversary," he says, "and partly because of the wonderful writing, so thick and deep.
"But I'm in a paradoxical situation. A year ago in Toronto I did Brian Friel's Molly Sweeney, which is all monologues. You sit there with the other actors, waiting for your cue, and then you're on for four pages. Right throughout the run I never stopped being scared, and I said `I'm never doing that again'. But now here I am in something even more exposing."
Like Krapp's memories, Neville's feelings on revisiting Nottingham after 30 years are tinged with sadness at how things change. "I can barely recognise the city. My beloved Pringle's Picture Palace, the cinema which was the Playhouse's first home and in which I played Macbeth, is now a Firkin pub. That was a terrible shock.
"Theatre in England has changed so much, too. I'm a Canadian citizen now and it's not for me to criticise my old country. But I ran a permanent company at the Playhouse, in repertory, and it's a great shame that that approach has disappeared - though I'm glad it's returning at the National. Too many young actors in Britain are just waiting by the telephone for a puny role in mediocre television."
His decision to take over as Playhouse director in 1963 caused a sensation far greater than the one that greeted the recent temporary defection of Ian McKellen (ironically a Neville protege) from London to Leeds. Back then, actors could be superstars without doing film or television and Neville, who rejected a seven-year Hollywood contract to dedicate himself to Shakespeare, was among the most famous. He and his great friend Richard Burton were the twin heart-throbs of the Old Vic company in the Fifties.
"We were idols," Neville says matter-of-factly, "and after shows would each have our own set of fans stretching down the Waterloo Road." When he cut short a triumphant West End run in the original production of Alfie and declared that he was heading for the Midlands "to get away from the pernicious idea that only the best should be in London", the press said he was crazy.
He not only played leading roles there (including Willy Loman in Death of a Salesman) he also directed Robert Ryan as Othello and the young Judi Dench as Saint Joan.
He speaks with equal pride of the Saturday morning youth club he started so as to build stronger community links: "We had 17-year-old miners playing trolls in scenes from Peer Gynt."
His childhood was spent in Willesden, north London, where his father was a motor mechanic and lorry driver. "We were quite poor and very, very working-class."
He was about to enter Rada in 1942 when his call-up papers arrived. For the remainder of the war he was a Royal Navy signalman, serving on battleships during the Normandy landings while simultaneously "training myself to lose my cockney accent, so that I could go home and do the classics".
At Rada, after he was demobbed, his accent was replaced by patrician vowels, but his father's values remained. "He always said `You don't buy anything, son, unless you've got the coppers in your pocket'." That governed his attitude to running theatres and helped him to ease a $4.5m (pounds 2.8m) deficit at Stratford Ontario, one of the three major Canadian theatres of which he was artistic director between 1973 and 1989.
He had decided to emigrate because he found the "can-do" mentality in the country's theatres "wildly exciting". He detects that same spirit in the students he directs in Toronto. They, of course, know him primarily through The X-Files, and rib him about the Well-Manicured Man's role as part of the shady committee that is in league with the aliens.
"I was originally meant to be in just two episodes, but the character was regularly brought back, because the audience simply doesn't know if he stands for good or evil." It's a mark of his professionalism that he can invest a line from The X-Files movie like "We are nothing but digestives for the creation of a new race of alien life forms" with as much gravitas as he would a soliloquy from Richard II, the play that earned him his finest reviews.
Seeing him acting opposite David Duchovny, or in a recent TV showing of The Adventures of Baron Munchausen - "six very tough months" - sets you thinking what might have happened if he'd stayed in Britain. Dench and McKellen have become Sir Ian and Dame Judi. Would he have become Sir John, ranked alongside Paul Scofield as one of our greatest theatre veterans?
"People have said that about the knighthood, but who knows? I have no regrets."
He does have thoughts of retirement. "Krapp may well be my last stage appearance. As I get older, the standards I set myself get higher - and I fall further short of them than I ever dreamed. I hate that. Acting's been my life. I've been successful and, at times, good at it, but now I'd sooner put my energy into directing."
There are plenty of plays he wants to stage. "Plays like The Revenger's Tragedy that a lot of people don't want to do," he says, enthusiastically. "I'm not a career director; I do plays because I have things to say about them and because one is supposed to stage things not to guarantee good box-office but to challenge the audience. I won't give up until I drop."
`Krapp's Last Tape' is at Nottingham Playhouse (0115-941 9419) from 11 to 13 March; `The X-Files' movie is available to buy on video from 29 March