I am due to meet David Lan upstairs in the Little Italy restaurant in Frith Street, Soho. It’s an elegant place that attracts the district’s media hotshots. Yet despite his own A-list celebrity connections, and despite being the artistic director of one of London’s leading theatres, Lan is not a natural member of the glitterati.

When he sits down, clad as usual in jacket and open-necked shirt (I don’t think I have ever seen him in a tie), and says “I’ve come here quite a few times, I love Soho”, it is clear he means the older, higgledy-piggledy, boho-Soho - not the modern, glamorous, central-London party zone.

Lan checks the menu. “I’ve a friend who says when you get given a menu, just lay it to one side, think what you’d really like to eat, and ask: ‘Have you got any…whatever it is?’ If the restaurant’s any good, they will. And if they haven’t, then you shouldn’t be eating there.”

But he admits that this high-maintenance approach is “not a rule I follow much” and in the end we both opt to start with the on-menu smoked mozzarella with Parma ham.

Over a glass of verdicchio, he begins to explain a bit about the remodelling of the Young Vic, which reopened in October last year after a ₤12.4m restoration.

“The original building was conceived in the late 1960s and opened in 1970. So we thought: ‘Do we need to stay true to the spirit or to the reality of what they actually built?’ We talked about working in that theatre, especially to people who’d been there right at the beginning. And, gratifyingly, often we said: ‘What we want to do is…‘ and they’d say: ‘That’s exactly what we would have done if we’d had the money.’”

The new main theatre feels familiar, but enhanced, while the remodelled building, to Lan’s relief, has been received “fantastically well. It’s curious, looking back on the reopening, it’s like getting married: part of your life that for so long was in the future and suddenly it’s in the past. People have said all the right things, they’ve said it feels like it’s always been there. Also it’s still standing, which is nice!”

He is conscious that the Young Vic needs to create a niche for itself, pointing to three recent and upcoming productions of The Seagull in London and Stratford-upon-Avon. “That’s fine if you want to see The Seagull, you’re very well looked after - we’ve got to do something a bit different.

“I’ve got very taken with the idea that what we do are ‘shows’, rather than ‘plays’. I think we should bring the term ‘show’ back from the cupboard; it’s a good word, provided we use it across the board, so that, say, Peter Brook’s touring show is a ‘show’ as much as Wicked [the West End musical] is a ‘show’. The showbusiness side is very important: we are in that world, it’s not an art-house world.”

Indeed, one of the architectural features of the wonderfully welcoming Young Vic is its glass frontage. It seems to flow into the community around it, which – with free tickets for local residents - it does.

And yet the first two productions in the main house seemed distinctly art-house. Both were operas by Jonathan Dove - first Tobias and the Angel (with a libretto by Lan), then The Enchanted Pig, a Christmas show based on folk tales. Nevertheless, they proved exuberant and inclusive (Tobias used a large supporting cast drawn from the local community). The shows did well both critically and commercially: “To get a bit grubby, they’ve all hit their financial targets,” Lan says. “But,” he adds, laughing, “I’m aware that success is only disaster deferred, so the next show is going to be disaster – and that’s mine…”

His first outing as a director in the new theatre begins previewing on Friday: Thomas Otway’s little known Restoration piece The Soldier’s Fortune. Lan describes the play as “terribly interesting about sex, but feels very naked, as if he [Otway] wrote it in a hurry and didn’t quite keep control of what he was writing”.

By now we are on to the main course. This is pan-fried black cod with lentils for Lan, but the waiter mishears my order (rigatoni with veal) and brings instead the day’s special, rigatoni with a duck ragu. Our conversation moves on to Lan’s life and career. “When I applied for the [Young Vic] gig at the end of 1999 I’m not sure I had any idea what I was letting myself in for. I directed ‘Tis Pity She’s a Whore there, which was only the second professional direction I’d ever done. I’d spent most of my life writing, but I’d always wanted to direct. Also a number of close friends of mine have been artistic directors, and I couldn’t quite see why they were doing it and I wasn’t.

“While I was rehearsing, my stage manager said: ‘Have you heard Tim [Supple, the previous artistic director] has resigned?’ And I remember thinking, well, I wonder who’ll take over, with no thought at all. Then over the next month or so one or two people said: ‘Are you interested in the job?’ And I thought, well, if you don’t get it, you don’t actually go to jail or have your tax increased or anything, so I went for it.”

He confesses bewilderment at “young directors who say: ‘This is how I feel at this early stage in my career.’ And you go, hang on a second, how do you know that? How do you know you’re going to have a career? [For me] it was just the thing that happened next.”

For Lan, directing was the thing that happened after writing and - in the middle of his period as a writer - several years spent studying anthropology. “I grew up in South Africa. I came to London, in ‘74, I think, and when I got here I felt that there was part of my life I didn’t really understand but that I wanted to…I applied to various courses and got into the one I wanted, at the LSE, and I had a number of very exciting years in the way that academic study should be.

“I just dropped out [of theatre] for a while. I spent a few years doing field research, and wrote a thesis that became a book.” His Guns and Rain: Guerrillas and Spirit Mediums in Zimbabwe is still in print.

As we wait for dessert, I take the conversation back to the theatre, and his friendship with the actor Jude Law, who was the highest-profile backer of the Young Vic’s rebuilding programme. “I thought that might come up,” smiles Lan. “There are many things about Jude. One is he’s a friend [Law had starred in Lan’s production of ‘Tis Pity She’s a Whore]. One is that he’s been a brilliant supporter during this whole period - he could have just put his name on a piece of paper, but he’s actually been around a great deal. I’ve been taking a lot of people round the theatre over the past months; if somebody’s really interested, it takes about 45 minutes to take them round, explain it all, answer their questions …Jude took an hour and a half. He just wanted to live it all: he’s a delight. He said he wanted to do something with us again, and that would be terrific; I’m sure he will – exactly what he’ll do and when he’ll do it I don’t know.” There’s a rumour that Law wants to play Hamlet, but Lan is unwilling to mention specifics.

In the summer of 2005, Lan found his West End production (sorry, show) of As You Like It hijacked by a tabloid newspaper storm surrounding Law and his then-fiancee Sienna Miller. Miller was playing the supporting role of Celia to Helen McCrory’s Rosalind. The Miller-Law relationship became a front-page fixture after news leaked that Law had had an affair with his children’s nanny, and Lan admits that the press interest “created pressure for people doing the show”.

“In a way the most curious thing that happened at that time was when Sienna took over the part of Rosalind. Helen was unwell, she couldn’t go on, and I was trying to sort out what to do when my telephone vibrated with Sienna saying: ‘I know the part.’ It’s a huge part, the biggest woman’s part in Shakespeare. I said, do you really want to do this? And she said yes, and she did really, really well. God knows, if she’d really screwed it up The Sun would have reported it, but she did it really well: it was very brave and very helpful to us.”

Dessert arrives: Lan has opted for a creme brulee, whereas I tuck into the most divine tiramisu I have ever tasted, only later realising that in fact I had virtuously ordered lemon sorbet. (Little Italy: where the waiters read your mind.) And so to the wrapping-up small-talk: are there any cherished projects Lan would like to turn to now? “Yeah, there are some. I won’t name them: if you have an idea, so has someone else. When I had the idea of doing A Raisin in the Sun [staged at the Young Vic in 2001], I was sitting in the Royal Court, and I saw a director reading another play by Lorraine Hansberry, and the moment I saw this I knew she was after A Raisin in the Sun. Next day I called the agent and said I really want to do that play, and a week later, she called me, and said Manchester Royal Exchange also want to do it, is that all right? Well, no! It’s a frustrating thing – it’s like there’s some sort of telepathy.”

Overall, though, he says: “What I’m interested in is finding ways of working with groups of people or companies who are on a different sort of journey from the one that we’re on or think we’re on.

“It’s not predictable as to how it will pan out – but it has been very exciting.”

‘The Soldier’s Fortune’ is at the Young Vic, London SE1 (020 7922 2922, www.youngvic.org), Friday to March 31.

…………………………………………………..

Little Italy, Soho, London W1

2 x chargrilled smoked mozzarella wrapped in Parma ham

1 x pan-fried black cod with braised Tuscan lentils, chilli and paprika

1 x rigatoni with duck ragu and pecorino Romano

1 x creme brulee

1 x tiramisu

1 x decaf cappuccino

2 x glass of white wine

Total: ₤101.30

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