It's no great surprise to learn that Nicholas Hytner will be leaving the National in 2015. All the same, it causes a pang of regret. He took over in 2003 when there was a sense that the National was drifting comfortably along without any sustaining vision. One of Hytner's great achievements – along with that of his executive director, Nick Starr, who will also be leaving in 2014 – is that he has restored to the theatre a strong sense of purpose.

How has he done it? First, and crucially, by making its work more available to large numbers of people. "The future of the theatre," the legendary Peter Brook said two decades ago, "is cheap seats." One of Hytner's first actions was to launch the Travelex £10 ticket scheme (now risen to £12) which meant a third of the Olivier's seats were available for the price of a cinema ticket: a brilliant pragamtic gesture that meant huge swaths of the audience for Hytner's 2003 Henry V were NT virgins. Equally important was the creation of NT Live, which broadcasts productions to screens around UK and the world, both live and pre-recorded. I remember going to the very first of these, Hytner's own production of Phèdre, with Helen Mirren, in 2009, and feeling it was revolutionary in its potential to enlarge the audience for drama. So it has proved: at a stroke, it has rescued the theatre from the charge that it is simply for the London elite.

It's one thing to open up the National. It is just as important to ensure the work itself is of the highest quality. And Hytner has done that by enlisting the support of some of the best living dramatists, and by ensuring that the National has been at the forefront of the argument about the state of the nation. His own opening production was a Henry V that reflected the turmoil over the Iraq war, and over the last decade we've had plays about the economic crisis, global warming and racial divisions. Everyone can come up with their own list of favourite NT shows. My own top five, in no special order, would be Howard Davies's breathtaking 2010 production of Bulgakov's The White Guard, David Hare's investigative Iraq play Stuff Happens, Lee Hall's much-loved The Pitmen Painters, and Hytner's own productions of Alan Bennett's The History Boys and Richard Bean's One Man, Two Guvnors. But, while they're all strong contenders, it's worth pointing out that Hytner has also embraced young, boundary-breaking companies such as Kneehigh and Punchdrunk, and sanctioned experimental work by directors such as Katie Mitchell.

Although I'm glad Hytner finally overcame his distaste for George Bernard Shaw, more might have been done to explore 20th-century British drama. But Hytner's achievement has been colossal, not just in expanding the National's audience and providing high-quality work, but in his readiness to act as spokesman for a British theatre threatened by insanely myopic government cuts.

Who should succeed him in 2015? You could make up a long list of names that would include Sam Mendes, Michael Grandage, Dominic Cooke, Rupert Goold, Marianne Elliott, Josie Rourke, Thea Sharrock, Jonathan Church and Howard Davies. But it's a measure of Hytner's success that whoever takes over will inherit a thriving theatre built on pragmatism and vision.