Lunch with a leading British actress in one of London’s finest restaurants would normally be a treat, but the thrill of meeting Samantha Morton at St John Bread and Wine in Spitalfields is tempered by the fact that: (a) she is, according to reports, a tetchy interviewee; (b) Mister Lonely, her new film and the reason for our meeting, is not particularly good; (c) I’m recovering from a vomiting bug and am concerned that pig’s spleen – St John specialises in offal – might not be a sensible way of returning to solids.

Issue (b) is a particular pain because it could otherwise provide a solution to (a). The standard approach to “difficult” interviewees is to witter inanely about a project at hand before venturing, gently, into more controversial areas, which in Morton’s case include her father’s marriage to her babysitter, her time spent in care and with a series of foster parents, and her tempestuous relationship with the tabloids.

Harmony Korine’s Mister Lonely, which recounts the story of a Michael Jackson impersonator who falls in love with a Marilyn Monroe double (played by Morton) and then follows her to a commune of impersonators in Scotland, offers no such opportunity for bland banter. The surreal art-house movie, which has a subplot involving a bunch of flying nuns, is beautifully filmed and forces you to think, but many of the questions it raises are drowned out – in the experience of this viewer – by irritation at its pretentiousness.

I spend my journey to East London, where Morton lives with her fiancé, Harry Holm, the director son of actor Sir Ian, and two daughters, aged eight and just six weeks old, fretting about how to broach the subject. Samantha, I thought you were the best thing in the film (true and often the case in Morton’s movies). Harmony Korine films are like Marmite: you either love them or hate them (definitely the case with Gummo and Julien Donkey-Boy). In the end, as Morton takes a seat, professing exhaustion but looking 70 times better than I feel, I go for the decidedly timid: “I think I may have missed the point.”

The 30-year-old actress glares back with an intensity that makes it immediately clear why she was picked to join the Central Television workshop for young people at the age of 12, and why she has since been sought out by directors ranging from Woody Allen to Steven Spielberg.

“How many times have you seen it?”

“Er…” The idea of watching it again gives me an instant headache. “Once… I mean, you were great as the Marilyn lookalike. I was just wondering whether you could…” I’m stammering now, “…explain it.”

She takes off her large black overcoat, places a napkin across her lap and puts her small hands on the edge of the table. “Those kinds of questions, with respect, are for the film-maker.” She still hasn’t blinked. Her intensely blue eyes are by far the brightest thing in the spartan dining room. “Personally, I found the film incredibly moving, but, equally, I walked away thinking, what did that mean? But I like that.” She orders a decaf Americano from the waitress hovering over us. “I’ve known Harmony since I was 18, and he’s someone I really admire because he constantly challenges the form in a way I find at times offensive, at times beautiful, but always intriguing. I hope the right people will go and see it.”

And that’s it. I’ve made my point (weakly). She has disagreed and responded (forcefully). And, when she begins examining the menu, it’s clear that, as far as she’s concerned, the discussion is over. This is what she’s like. Essentially, she doesn’t especially care what people think about her work. And while some may interpret this as aggression, I think it’s just incredible self-confidence.

Tellingly, the woman who once turned up at a Buckingham Palace garden party in flip-flops, and famously asked Woody Allen to see the script when he wanted to cast her as a mute in Sweet and Lowdown, goes on to remark that the only errors she has made with roles have occurred when she has been bullied by others. “Mistakes have happened when I haven’t followed my gut instinct.”

The self-assurance extends to her choice of restaurant. I glance at the menu and feel a wave of nausea. Jellied pig’s head. Confit duck gizzard. Devilled kidneys. The room has the air of a butchery, and even some of the puddings – blood-orange jelly – sound like they’ve been made from ingredients gathered from an abattoir floor. Perhaps sensing my squeamishness, Morton interjects.

“They do great fish and salads here, too. I’m actually vegetarian, but, you know, if I did eat meat I would eat it in its entirety.”

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