Women on the verge: Hattie Morahan and Ibsen's Nora

Nora in A Doll's House is right up there on the list of big theatrical roles for women; Henrik Ibsen's 1879 play provides a richly complex female central character, who ultimately leaves her babying, patronising husband – and her children – so she can discover who she really is. The play has also, of course, been seen as a game-changer in feminist literature and, for its move towards realism, in theatre history.

Not that knowing that is all that helpful for any actress tackling Nora. Hattie Morahan played the role in a production directed by Carrie Cracknell at the Young Vic theatre in London last year; the show was such a hit, it's about to be revived with much the same cast. She confesses she was "both daunted and excited" to take on the part, adding that "It feels a real honour. It's a part that is written about because of the history of feminism, and of theatre… [But] you actually just have to shed that; Nora doesn't know she's an iconic part, or that her door slam is reverberating through history. You just go – OK, that's for other people to talk about."

Talk about the play people certainly did – Simon Stephens' fresh, crisp new translation was well received, while the revolving stage Cracknell set it on was more divisive – but much of the chatter was reserved for Morahan's impressive performance. Kate Bassett in The Independent on Sunday called her "a great actress in the making, if not of that rank already," while The Sunday Telegraph deemed it an "once-in-a-lifetime performance." Then Morahan won best actress at the Evening Standard theatre awards in November – seeing off formidable competition from Cate Blanchett, Eileen Atkins and Laurie Metcalf – as well as netting a Critics' Circle award. Yesterday, she was nominated for best actress at the Olivier awards too – raising the distinct possibility of a Hattie hat-trick.

Meeting Morahan at the Young Vic, the week before a fortnight's refresher rehearsal period, she still claims to have been completely blown away by the wins. "I really wasn't expecting it. You absorb it after several months… but thinking back, gosh, it's incredibly nice." She's eloquent, intelligent, but well-spoken in the slightly old fashioned sense, her speech littered with jolly-hockey-sticks "gosh" and "blimey".

This humbleness continues with a clear-sighted, if self-deprecating, understanding of the way that such awards tend to work: "If you do something headline like Nora in A Doll's House, people go 'ooh, should we give them an award?' In many respects it's nonsense, but I'm utterly thankful, and so honoured."

Morahan herself is strikingly open to more experimental theatre. After getting a degree at Cambridge, she leapt straight into working as an actress (a season at the RSC, nice break if you can get it), and then did four productions with theatrical iconoclast Katie Mitchell, which she loved. "I hadn't trained [at drama school], so it was the first time I'd encountered any structured approach to getting under the skin of a play or a character. [Mitchell has] rigour and good humour and strength of vision… she's just a brilliant being really."

Some of the shows – such as Mitchell's take on Chekhov's The Seagull – were not always well received. Morahan suggests that with such physical, "more European" ways of staging plays, it takes a while to tune your brain in – a process she enjoys, but which some people seem to resist. "In this country, there's such a tradition of 'the word is sacrosanct' and people standing on stage and delivering clever writing in a way that isn't always about absolutely coherent psychological truth but about" – here she adopts a plummy theatricality – "letting the play be heard".

Things may be changing, however. Morahan mulls over her hunch that there's a new generation of theatre audiences – and practitioners – who have grown up on a diet of experimental fare: "I think things will shift; people are more open."

Her own background means that Morahan has had plenty of experience of sitting in the stalls; her mother is an actress, Anna Carteret, while her father, Christopher Morahan, is a theatre, TV and film director. She was taken to the theatre a lot as a child, and confirms that it was always the career path she wanted – laughing at the idea of herself as a pompous 10-year-old, watching plays, taking note, plotting how she would play a part…

"I just caught the bug," she says.

Her parents must have been particularly proud of her performance in A Doll's House – for Morahan's mum played Nora herself in the Eighties. "She said, just honour all the different facets of the character – because she's massively multifaceted – rather than trying to condense her into a uniform whole. Part of the key to her is the varied prisms through which we see her."

Although the theatre is her first love – she received glowing notices for her equally multi-faceted, and supremely moving, role as poet Edward Thomas's exasperated wife Helen in The Dark Earth and the Light Sky at the Almeida recently – Morahan also impressed with a subtle performance as Elinor Dashwood in the BBC's Sense & Sensibility in 2008, and appeared in a high-stakes adaptation of Martin Amis's Money.

Then there was a main part in ITV's underrated Eternal Law last year: a sort of metaphysical courtroom drama, it centred on a pair of angels sent to earth to help humans by working as, erm, lawyers. It may, Morahan ponders, have been too much of a "way out" concept, and was cancelled after only one series – despite deliciously devilish performances from fellow stars Tobias Menzies and Sam West.

And many people will recognise her from a small but recurring, and very funny, part in the BBC's hugely popular sitcom Outnumbered, in which she plays the completely hopeless Jane. Morahan also appears in a film due out in June: Summer in February tells the story of a love triangle in the Newlyn artist colony in Cornwall at the start of the 20th century; Morahan plays the painter Laura Knight, and her co-stars include Emily Browning, Dan Stevens and Dominic Cooper.

Morahan got to spend a couple of months shooting in Cornwall, which sounds rather lovely, but home is usually Finsbury Park in north London (although she's trying to move, and after the interview explains she's off home to get stuck into some DIY). She lives with her fiancé, Blake Ritson – although it is, she explains, a very long engagement: "we haven't done anything about it – we've been engaged for about seven years! It's a totally long, very nice, sort of aimless engagement."

Ritson, who she met at Cambridge, is also an actor and film-maker: "It could be very difficult – a lot of people say 'oh god, I could never go out with another actor' – but actually I think it's more helpful than not."

For now, Morahan's attention is on revisiting A Doll's House, a rare chance to return to a stage production – although she has, she explains with her voice rising an octave or two, been "slightly in denial" about re-learning the lines and stepping back inside that revolving house. "I've no idea how much will come back. But I'm really, really excited because it was just so exhilarating to play that journey every night. The part is bonkers – but really fun to do."

'A Doll's House', Young Vic, London SE1 (020 7922 2922; youngvic.org) 28 March to 20 April; 'Summer in February' is released on 14 June