Vicky Featherstone is the only artistic director of the National Theatre of Scotland the country has ever had.

And now she is leaving, handing the reins to another bright and talented director, Laurie Sansom. When we meet, she admits she is "a bit wobbly". Featherstone and her family have just moved out of the house they shared since the NTS was launched in 2006. In the coming weeks, she will move to London to take the helm at the Royal Court Theatre.

She is warm, sharp, clever and sometimes outspoken, besides being a lauded and excellent director. But at first Featherstone was, in some quarters, a surprise choice to be the first director of a national theatre which had been desired by many for so long. Six years later, the NTS is a respected producer of acclaimed plays such as Black Watch, The Strange Undoing Of Prudencia Hart, Peer Gynt and Macbeth.

We are talking over tea and biscuits in her snug office at the NTS's modest offices at Spiers Lock in Glasgow. Featherstone is calm but clearly emotional. "This is my last morning in our house, so I feel wobbly today. I am sad to go, and I am leaving sooner than I thought I would. When I took the job, I said to my husband [Danny Brown]: 'After five years we will decide whether it is appropriate or not for our family to stay.' But, of course, five years came and went, and we were loving it so much, and loving living in Glasgow so much, we didn't even ask the question. I am pleased I am leaving before I have started to become frustrated or lose my energy on it, so I feel I am leaving ahead of time, which is good but also means I am feeling grief about it."

The NTS has come a long way since Featherstone first walked into an empty temporary office in Hope Street knowing she had to start a national performing company from scratch. Now its shows are touring the globe. Black Watch is a worldwide theatrical success. Shows such as Alan Cumming's Macbeth, David Greig's Prudencia Hart, Frantic Assembly's Beautiful Burnout and her own Enquirer, and recruiting the talent of people such as Greig and David Harrower, directors such as John Tiffany and Graham McLaren, and actors such as Cumming and Ian McDiarmid, have elevated the company to the status of theatrical powerhouse.

Not that it has all been easy for Featherstone. Juggling motherhood – her son is now 13, her daughter 11 – with such a demanding job is one challenge. Setting up a national company, in a land with a strong tradition of theatre, playwrights and writers, and after many years of campaigns calling for a national theatre, is another. "It has been totally life changing," she says of her tenure. "It has been hard. I have thought more and worked harder than I ever thought possible, as has everybody who works here. It has been incredibly inspiring.

"There was a 'zero' moment – walking into my office with my mobile phone and a Muji notebook, no furniture and a copy of The Herald. I was sitting on the floor, reading the paper, with my notebook, and thinking: 'I have got to start a national theatre.' If I had thought about what that meant historically, it would have been terrifying, but I just had to go and take the task in hand. So in a way it seems surprising to me that we have done it, from nothing."

There was no red carpet and celebrity guest-list for the company's opening salvo. Instead she launched the NTS with Home, in which 10 venues around Scotland simultaneously staged work by 10 writers and directors. "I presented it to the board," she says, "and because they couldn't imagine it, they were unsure whether it would work, but they trusted me and that was an incredible vote of confidence from them."

Later in 2006, on a temporary stage at a drill hall in Edinburgh, came the rousing and devastating Black Watch. Gregory Burke's play, directed by Tiffany, is now NTS's touchstone production and is still touring around the world. There was a sense a few years ago that even the NTS was tiring of its success but Featherstone will have none of it.

"I feel relieved we have Black Watch and I adore it," she says. "I have never felt insecure that we are the company that made Black Watch – I would rather that than people not knowing who we were. It is an extraordinary piece of theatre. Every time I see it I think, 'God, it is still ahead of its time.' But even more than that, the visceral effect it has on the audience reaffirms theatre again and again." I ask whether other productions have been as good as Black Watch in her view. "We've done loads. Christmas Carol is that good, Men Should Weep, The Wheel, Prudencia Hart, Peer Gynt and Macbeth – there are a lot that I think are an A-plus. What is interesting is that the work which has been new and could only have been made by us has really worked, and the work that has been fantastic but other companies could have done, people haven't been as interested in."

Featherstone is English. Born in Surrey, she lived in Alva, Clackmannanshire, until she was seven and her father's work took the family around the world. She gained a degree in English and drama at Manchester University, going on to direct in theatres in the north of England before establishing a reputation as the director of touring company Paines Plough. Although remarked upon on her arrival in Scotland, her Englishness suddenly became an issue three years ago.

Without naming specific articles or writers, she began to feel it was a tool being used to beat her. It became, she says, "a thing". There were more references made to her background in newspaper stories, letters and journal articles. Some commentators felt she was deliberately ignoring old Scottish plays. And it became a "thing" that temporarily threatened to derail her. She has not spoken about this difficult period of her tenure before, and she chooses her words carefully.

"I'm sure it was a thing from the beginning but nobody ever communicated it to me. It became a thing, interestingly, because people didn't like my programming. And rather than articulating that, it was easier to say the reason my programming was wrong for Scotland was because I am English and therefore don't understand how to programme for Scotland," she says. "For me, when I started, the task was to prove Scotland could create and sustain an outward-looking, modern, contemporary national theatre, and that is what my task was. We needed to get to a level where we had proven it was world class before it was time to turn to the past, so we could turn to the past from a position of status and power.

"It really upset me, because, as with all kinds of bullying, you don't have a voice – so the hardest thing for me was that if people had criticised the programme, I could have defended it, but when people are criticising the programme because I am English, that is indefensible. What it did, for a short period of time, was paralyse me from being able to be make artistic decisions and I felt defensive. This is about three years ago. And I had a period – not long, because I am very strong – of a few weeks where I thought, 'I cannot do this job – I don't know how to do it,' that I wasn't the right person for it, and I questioned myself because I didn't know how to make decisions any more."

After a pause, she adds: "In the end I had to have a strict meeting with myself and made the decision to either feel this attrition whittling away at my confidence or go out and deal with it. So that's where I had the idea of Staging The Nation [a series of NTS events in 2011 debating older plays], because what I realised was that this wasn't my discussion – it was about a discussion that Scotland needed to have that I felt part of."

She met with one of her fiercest critics, the writer Paul Henderson Scott, who despite tackling her on the subject of not staging Scottish plays, had never attacked her personally. She went to his house in Edinburgh for tea to discuss Scottish history and theatre. "He had been the harshest critic, or the most persistent, but he was [adamant] that he wasn't anti-English. We had an amazing conversation which was inspiring. It was a massive maturing and learning process."

She adds: "People writing in newspapers have incredible power, and it was beginning to damage me, but then I met Mr Scott and I thought, 'Actually, I do have the power.' I always felt it was from a small group of people and did not actually represent the relationships that we had created around the rest of Scotland."

Now Featherstone is once again confident in her abilities, and the slate for the National Theatre for much of 2013 is already in place, including a theatrical version of the vampire film Let The Right One In by John Ajvide Lindquist. Her successor, Sansom, who was in Glasgow last week for meetings and flat-hunting, will have time to settle in and find out more about Scotland and its theatre. She believes he is a "brilliant theatre maker, and he understands what we are doing".

Although she is heading for Sloane Square, it seems a large part of her will remain in Scotland and its "incredible artistic community". The country's national theatre will endure and prosper beyond the departure of its founding director. "I am not being disingenuous; I am not being falsely humble," she says, "but there are systems in place that mean some brilliant people can make decisions without me being there, and things can move on."

Vicky Featherstone, Artistic director, National Theatre of Scotland