You wait ages for a top job in British theatre – and then 11 come along at once. When, back in the autumn of 2010, Michael Grandage decided to quit as artistic director of the Donmar Warehouse in London, few could have guessed that so many others in the profession would join the scramble. Rachel Kavanaugh at Birmingham Rep was off a few months later. The following July, Nicolas Kent announced he was leaving London's tiny but powerful Tricycle after 28 years, rapidly followed by the artistic director of Scotland's Traverse. In October 2011, the top spots at the Royal Shakespeare Company fell vacant, followed in December by their equivalents at the Royal Court.

It's probably pushing things to describe the artistic directors who've stepped in to replace them as an avalanche – with extensive notice periods, it's more like a steady trickle – but it's nonetheless striking that, in the last 12 months, many of the UK's most important theatres, from regional hubs such as the West Yorkshire Playhouse to the National Theatre of Scotland (NTS), have come under fresh, and significantly younger, management. When the maverick director Rupert Goold was announced as the incoming boss of the Almeida just over a week ago, it seemed like a sign: the old guard was gone. A new generation is here.

It's a fascinating moment to take stock, not least because so many things in British theatre feel in flux. What's on these new artistic directors' minds? What do they want to change? Can we expect a big shake-up? Will audiences even notice?

To find out, we took five as our sample: Indhu Rubasingham, who took over at the Tricycle last summer; Erica Whyman, 43, the RSC's new deputy artistic director; Vicky Featherstone, 45, shortly to take the reins at the Royal Court; and Laurie Sansom, 40, about to succeed Featherstone at the NTS. It's a good mix: two national companies, one based in Stratford, one in Glasgow; the UK's leading new-writing theatre (Royal Court); and a boutique venue in London's most diverse borough (the Tricycle in Brent). For balance, we added a commercial theatre producer: the hotly tipped Eleanor Lloyd, 33, who scored a West End hit with 2011's Butley, with Dominic West as a lecturer whose life is falling apart. Rubasingham offers to host us at the Tricycle.

So does it feel like power is shifting? Rubasingham nods. "I think it is a generational thing. As colleagues, we've grown up together, we've had fights together." Sansom agrees. "Over the last few years, a much more eclectic group of people have been given leading positions. It began a while back, so I feel like we're inheriting it. Different artists are being allowed into what felt like a closed establishment club."

Whyman's arrival is particularly eyecatching: while the main job at the RSC went to an old hand, Gregory Doran, the enthusiasm that greeted her appointment was a sign that the company was at last looking outside itself, thinking hard about how to get younger people through the door. "It's about working with a new generation of theatre-makers," she says, "and finding a really interesting audience that hasn't always been attracted to Stratford. It would be great to get them to make work with us."

Everyone agrees that some of the rivalries that have divided British theatre (fringe versus mainstream, regional versus metropolitan, amateur versus professional, subsidised versus commercial) have started to break down. The National and the RSC have made fortunes by touring War Horse and Matilda to the commercial sector (the National will have an unprecedented four shows in the West End this spring); and producers like Lloyd work with taxpayer-funded companies as often as they do with independent investors. Thinking in terms of competition isn't helpful, she says – it's better for everyone to realise they're in the same boat. "I don't think audiences make that distinction. They don't realise we're different, or indeed that we're funded differently. They go to the theatre, that's that."

It's an intriguing question, though: what do we mean by theatre in 2013? Live broadcasts online and to cinemas have revolutionised the way audiences experience stage drama: last year, National Theatre Wales combined live streaming with an audience comment feed for a new play about Bradley Manning, the US soldier accused of passing material to WikiLeaks; it reached 76 countries. Meanwhile, its Scottish cousin has pioneered epic cycles of five-minute dramas, transmitted live on the web as they were performed across Scotland. The Guardian has got in on the act, too, co-producing with London's Young Vic two short films based on plays staged at the theatre; these include Nora, which reimagined the heroine of Ibsen's A Doll's House as an ad executive struggling to balance work and family.

Do traditional theatres risk being left behind? "Watch this space, because the RSC are going to be very ambitious," says Whyman. Lloyd thinks we'll see much more live broadcast: the first cinema broadcast of a West End opening night took place just last Thursday (the play was Great Expectations at the 690-seat Vaudeville theatre). But Rubasingham says it's tougher for organisations like the Tricycle. "I'm ambitious, but I don't have the resources. Digital requires a lot of expense." Although Vicky Featherstone admits live broadcasts have opened up a new world, she says: "I would never want to do that at the expense of touring. What digital is amazing at is access – it's not intimidating in a way that live theatre can be." She admits she'd love to have livestreamed Mark Rylance's barnstorming performance in Jerusalem, something her predecessors refused to do.

Vicky Featherstone, incoming artistic director of the Royal Court. Photograph: Sarah Lee for the Guardian

But is theatre even happening in the right places to begin with? With the £113m revamp of its main stage now complete, Whyman's RSC is hurriedly working out how to bring back its experimental studio space, The Other Place. And, while the builders are hard at work at the National, the theatre has opened a temporary stage called The Shed for more offbeam work. Everyone here is nervily aware of the success immersive groups have had in making theatre in temporary or site-specific spaces. This is a live issue for Featherstone, whose success with the NTS – which has no permanent home – caused some to question whether theatre companies actually need theatres at all. "Not having a building makes you really focus on the work," she says. "Being in Scotland taught me that. That doesn't mean that the Royal Court won't be putting plays on stage – of course it will. But we've got to think about that more."

One alternative is playing at festivals: various theatres have performed at Latitude, and Whyman created a residency for her previous company, Northern Stage, at last year's Edinburgh fringe. The Court has dabbled with pop-up work in Elephant & Castle and Peckham, south London. Theatre Local, as the project was called, combined plays with events and drop-in workshops, all done in close consultation with the local community. Featherstone's eyes shine. "It felt like Berlin in the late 80s and early 90s – theatre, events, all-night clubs."

If it's a surprise to have a Royal Court director praising club nights, it's not just because this new generation are younger – it's also because they are a visibly more diverse bunch. The story that an American producer once joked about UK theatre being entirely run by "men called Peter" is probably apocryphal, but it's interesting, I say, that Sansom and I are the only blokes in the room. Is it significant that more women, to choose one obvious yardstick, are running major theatres? "Some of the best commercial producers are women," Lloyd says, "and there's lots coming up, so it doesn't feel like a thing."

Sansom argues that there are more women at the helm of major subsidised theatres, too. Whyman nods. "Yes, the culture is shifting. The boy-genius culture with directors – that felt very male. I remember when I had three assistant directors at [west London's] Gate theatre: two women and a man, all about the same age. They went for interviews at a distinguished theatre I won't name. He was asked why he'd done so much assisting, and they were asked why they hadn't done enough. They had done exactly the same amount."

Rubasingham, born in Sheffield to Sri Lankan parents, says it isn't just about gender. She's weary of being asked about her own ethnicity. "When people say, 'What's it like being an Asian woman?' I want to say, 'Tell me what it's like to be white!'" But she has nonetheless been very vocal about the Tricycle's need to find an audience as diverse as its location – a question that could equally be asked at theatres up and down the UK.

Entwined with these problems, of course, is the thorniest of all: money. Arts Council England has already had its budget cut by a third to £350m, and there are more cuts coming – all but certain to be passed on to arts organisations. As the culture secretary Maria Miller has insisted, the arts shouldn't consider themselves a special case.

Rubasingham and Lloyd emphasise that national funding isn't the whole picture: regional theatres, many reliant on local authority cash, are especially vulnerable as councils look for programmes to cut. In Newcastle, the Labour council threatened to axe the city's arts budget by 100%, and Westminster council followed suit, with others proposing huge cuts (in Newcastle, the scandal was such that Harriet Harman, shadow culture secretary, was forced to intervene). Whyman, who lived in Newcastle until last December, has been at the sharp end. "I've sat with civic and business people saying, 'Isn't this fantastic, the cultural regeneration and infrastructure we've done?' But the minute resources were scarce, culture remained at the bottom of the list."

How would she make the case differently? "I want to have an argument about quality of life. Why are we intent on decimating quality of life in our big northern cities and in great chunks of London?" Rubasingham agrees: "It's about the value of the arts – at ground level, on the high street – to disenfranchised young people. What's frustrating is that we're the best in the world at this stuff, culture, and it's such a tiny amount of money." She laughs. "Give us 1% of your defence budget and it'd be a start." Featherstone says: "We're not asking for more. We're just asking to be valued as an important part of a healthy society."

Sansom's challenge is different: for all that the Scottish arts scene has had its woes (the head of Creative Scotland recently resigned after bungled funding changes), arts cuts are less wounding. North of Carlisle, he says, there's a sense that culture is something to take pride in, particularly as Scotland faces an independence referendum: "No one is looking to challenge the value of a strong cultural identity, irrespective of where you are on the debate." Whyman looks deadpan. "We could learn from that in England."

I ask about immediate worries: they say access, fear of taking risks, apathy, changes to education. And what are they excited about? Sansom: "Increasing interactivity." Lloyd: "A great year of shows in the West End." Featherstone: "Every time someone at the Royal Court writes a new play, it moves us on in some way." Rubasingham: "The world is getting smaller."