The "10" will take him up to 2013, which is coincidentally also the year of the National's 50th birthday. The "year or two after" will take him up to the end of the National's capital project which will see the Cottesloe stage close for a year and then re-open, rebuilt as the Dorfman. The theatre will be named after Jewish philanthropist Lloyd Dorfman who is also chairman of Travelex, sponsor of the National's cheap ticket seasons - currently set at £12. This is the mainstay of Hytner's project to democratise theatre and broaden the National's audience. It is all part of a grand objective: to create good work that is - to use two overused words favoured by theatre types - accessible and relevant.
"As a director I've always felt you have got to have as your cornerstone the desire to be more than a niche art form. That's a ghastly term - but if the theatre stops speaking to the wider public, if it becomes part of an enclosed conversation, it will ultimately shrivel," he says.
Relaxing with a cup of tea, Hytner exudes exactly the kind of reassuring calm that it takes to run a theatre as complex as the National, let alone direct shows as manic as One Man, Two Guvnors, or as thrilling as his 2010 "police state" Hamlet. Beyond his desk is a magnificent panoramic view of London that is bisected by the Thames. A buzz of human traffic filters up from the South Bank below, while from above, another kind of buzz drifts down from police helicopters monitoring student, union and Occupy London protests on the north side of the river. These are turbulent times, the kind of times that, under Hytner, the National Theatre has sought to reflect.
"It is important to occupy our big stages with work that is entirely connected to the world we're part of and moment we're living through," he says. It may look like a mission statement on the page. But when he says it, it sounds like real belief.
So alongside classics and huge international hits such as The History Boys and Warhorse, both of which have transferred to Broadway, National Theatre plays under Hytner's watch have covered subjects as urgent as the wars in Iraq and Afghanistan, and the financial crisis.
More recently he has staged the global-warming play, Greenland, which received what can only be described as a right kicking from the critics. But for Hytner if the critics are important, they are certainly not all-important.
"It cuts all sorts of ways. There have been shows - I'm not going to say which ones - where I have been astonished by how positive the critical response has been," he says phlegmatically.
But there is another group of plays that under his directorship has perhaps been more prevalent than ever at the National. It is a category of work that might be called the Jewish-interest play. And we are not talking about new productions of old material such as The Merchant of Venice. This is new work: Ryan Craig's Edgware-set The Holy Rosenbergs; Tadeusz Słobodzianek's Holocaust play Our Class (translated by Craig); Mike Leigh's Two Thousand Years. Or what about Primo, Antony Sher's adaptation of Primo Levi's If This Is A Man? Then there is Richard Bean's East End immigration play, England People Very Nice, which, along with almost every other ethnic stereotype under the sun, featured hora-dancing Chasids. In fact, has there ever been a time when Jews have been represented on the National's stages as much as they have under Hytner?
And, just to pre-empt the inevitable "ah ha!" from those who can detect Jewish "media influence" in an Irish jig, not all these plays have been universally praised by Jews. Some took exception to the way The Holy Rosenbergs represented a Jewish family who did not stop arguing about Israel even while they prepared for the funeral of their son.
"I don't know," says Hytner, by which he means that he does not know if his illustrious National Theatre predecessors - in reverse order Sirs Trevor Nunn, Richard Eyre, Peter Hall and Laurence Oliver - programmed many plays of particular Jewish interest. But he also means he is not even aware that he has."I don't think I've gone out specifically to look for material of Jewish interest," he says when I put the list to him.
"There are a lot of people here who are involved in the construction of the repertoire and I don't think any of the plays you have mentioned have been championed by me alone in the teeth of opposition or even indifference from the rest of the team."
Fair enough. But still, could it be true that under the National's first Jewish artistic director, plays with Jewish themes have been more likely to get an outing than ever before? There appears to be not the slightest flicker of recognition from Hytner at the suggestion.
"I did not know before Mike [Leigh] started on Two Thousand Years that the subject matter was a contemporary Jewish family," he continues. "So anybody who asked Mike to do a play would have got Two Thousand Years."
Suddenly this line of questioning seems rather silly. Work produced by directors and artistic directors is not a reflection of who they are in the same way that it often is with writers. I mean, Hytner also happens to be gay, but any suggestion that the National is staging more plays of specifically gay interest would be completely barmy. Yet there have been moments during the past eight years when Hytner's Jewishness has been connected to the work produced at National, and not always in a way that Hytner would have liked. When in 2008 he programmed David Hare's play about New Labour, Gethsemane (directed by Howard Davies), there were accusations that the main character, which in the run-up to the opening was said to be based on Lord Levy, was antisemitic. Hytner rubbished the accusations. But what appall-ed him was the notion that he, of all people, was capable of choosing a play with an anti-semitic character. "When I say I'm Jewish, I take it seriously. It's important to me and I'm proud of it," he told me back then.
On another, happier occasion we happened to speak the day after the opening of his revival of Dion Boucicault's caper, London Assurance. Starring Simon Russell Beale and Fiona Shaw, the production featured a brilliant script makeover by that man Richard Bean, which turned a Victorian antisemitic gag into a gag about Victorian antisemites. Hytner was on a high, and not only because his production was a triumph.
"What about that for a complete undermining of Victorian antisemitism?" he trilled.
Back in his Thames-side office he puts his answer on hold while he pauses for thought - a Hytner trait.
"But look," he resumes eventually, "I am totally delighted to have put those plays on. It interests me that people have wanted to create material that is of specific relevance to a Jewish audience. Although I should say, I wouldn't programme anything if I thought it was only of interest to a Jewish audience - or any demographic. Well, not any. I've cheerfully programmed for the four to six-year-old demographic."
Toddlers aside, if there is an outlook that informs which plays he chooses to stage or direct, it is that theatre should engage the wider public. Commercial producers would agree, which is why the West End is full of juke-box musicals. But with Hytner it is an outlook that leads to work that is both stimulating and hugely popular. One Man, Two Guvnors is a good example. It is brimful of slapstic and Bean one-liners, yet it is culturally very knowing. Though rooted in the Italian commedia dell'arte tradition, it is populated with variety and Carry On archetypes.
The show may also give a hint as to the path Hytner might take after he leaves the National. He sees no reason why such a production could not have been created in the West End rather than in the subsidised theatre.
"I don't want to stop entirely being an impresario," he says. "And I don't want to stop working with some of the people I work with here. I would be interested to see if there is a way of putting stuff together in the commercial theatre in a way that is a little more like it used to be. Looking back at One Man - my God that was a commercial project. Anybody could have done that. Anybody on the other side of the river [by which he means the West End] could have the conversations we had."
Whenever he leaves, the National will be in rude health, not just artistically, but commercially. The New York production of Warhorse is pulling in a million dollars per week. Unlike some of his predecessors, Hytner does not take a cut of the box office with the shows, such as The History Boys, that he directs. "I don't take it because there is a clear conflict of interest. I would have felt uncomfortable. If I'm investing the National Theatre's money into something, I can't be investing it on my own behalf. So I don't."
Before he departs there are many more plays to produce and direct. An Othello starring Adrian Lester and Rory Kinnear beckons. Soon he will begin rehearsing with Antony Sher for a new play by Nicholas Wright called Travelling Light. It is, in every sense, a Jewish play. Hytner describes it as a "parallel reality" play. It is a tribute to the culture that gave rise to Hollywood, even though it is mostly set in a Lithuanian shtetl.
"It's hilarious," chuckles Hytner. "It's about a lot of argumentative Jews who are inventing the movies and they don't even know that they are dong it. Nick [Wright] is not Jewish but the script is pitch perfect, and it's directed by me. And I'll tell you what's lovely - to have a play about Jews which is not about the Holocaust, which is not about Israel, and is not about antisemitism."
And then, after another pause and a glance towards the view which will surely be missed when he eventually hands over the greatest job in theatre to someone else, he says: "I think the reason I wanted to do Travelling Light was because I'm Jewish."
