Meryl Streep and Alec Baldwin are sitting on identical high-backed chairs in a reception room at the Plaza hotel, just off Central Park, in New York. Streep is sipping a gin martini, “Very dry, with a twist”, which seems perfect; Baldwin’s “water and an iced tea” less so. An Irish whiskey might have been more appropriate. She’s in a black dress, he’s in a dark striped suit. It’s early evening, between the red-carpet premiere and the reception for their new film, It’s Complicated. Baldwin, 51, is big and loud and expansive, with a fabulously rich, deep voice that can quickly fall to a seductive growl, and an infectious Irish love of the grand story, true or not. Streep is effortlessly regal, a touch prickly, acidly witty, giving as good as she gets, often dissolving into hoots of laughter. It seems astonishing that Streep, 60, is at the pinnacle of a career that has had many pinnacles. She has won two Academy Awards – best supporting actress for Kramer vs Kramer in 1980, best actress for Sophie’s Choice in 1983 – and has received 15 Oscar nominations, more than any actor in history. Who doesn’t think she’s the greatest living American actress? With nothing left to prove, she is having a ball, throwing caution to the wind in films such as Mamma Mia!, the musical that became one of the most successful films of all time in the UK; The Devil Wears Prada, playing a deliciously icy facsimile of the American Vogue editor, Anna Wintour; and Julie & Julia, for which she looks certain to get another best actress Oscar nomination as Julia Child, the large, and larger-than-life, doyenne of American cuisine, with Stanley Tucci as her bald and much shorter husband. In real life, as they say, Streep has been married for 31 years to Don Gummer, a sculptor, with whom she has four grown children.

The very least one can say about Baldwin is that he is the best actor on American television today. His Emmy wins in the past two years – as outstanding lead actor in a comedy series, playing Jack Donaghy, an egotistical right-wing tele-vision executive and Tina Fey’s boss on 30 Rock – testify to that. Yet Baldwin is a man of powerful appetites and heady, often contradictory, ambitions, recently judging his whole film career a “complete failure” and vowing to give up on Hollywood because he despises every movie he has ever been in, and himself in them. You must have impossibly high standards to see Glengarry Glen Ross, or The Cooler, for which he won an Oscar nomination, as failures. Still, tonight, for my benefit – actually, for that of Streep, whom he obviously reveres – he’s making a damn good show of having enjoyed doing this film. In his real life, Baldwin is known for his brutally public divorce from the actress Kim Basinger. He has fought a long battle for time with their daughter, which has made him a vocal advocate of fathers’ rights. It’s fascinating to see two such different actors, such different people, working together for the first time. It’s Complicated, a romantic comedy, has a slew of refreshing twists. Streep plays Jane, the owner of a fancy bakery and restaurant. Baldwin plays Jake, her ex-husband, a charming, roguish lawyer. They’ve been divorced for 10 years, ever since Jake ran off with a much younger woman, to whom he is now married. Jane and Jake have three grown-up children. After years of barely speaking to each other, Jane and Jake find themselves unexpectedly spending the evening together out of town, at their son’s graduation. After they have knocked back far too many drinks, the evening turns into a passionate, sweaty night. Before they know it, they are having a full-blown affair. It’s Complicated is written and directed by Nancy Meyers, who has carved out a unique niche in Hollywood with romantic comedies about, and for, real – ie, older – people, including What Women Want, starring Mel Gibson as a man who can hear what women are thinking, and Something’s Gotta Give, in which Jack Nicholson finally ends up with an age-appropriate partner, Diane Keaton. One of the main pleasures of It’s Complicated is watching older – well, somewhat older – people having a proper physical, sexual relationship in a big studio movie. Yes, there’s flesh: more than a hint of Streep’s, and a barrelful of Baldwin’s. The two of them spark off each other so well, it seems best to give you their patter straight, as it happened.

Christopher Goodwin: The conventional wisdom in Hollywood is that films for older audiences, particularly for older women, don’t make money.

Meryl Streep: Oh, do we have to talk about conventional wisdom? Why are films about young people for all people, when films about older people are only for older people? Why is that? That’s a more interesting question. You know what? A laugh is a laugh.

Alec Baldwin: I feel funny because yes, I’m older than I was, but people say “older” like I’m George Burns or Walter Matthau.

Streep: And he’s way younger than I am. But things have changed. Bette Davis was 40 – 20 years younger than I am – when she made All About Eve. And she was saying she was washed up. She took the famous ad in Backstage – “Actress. Multiple Academy Awards. Looking for work.”

One of the moments in It’s Complicated that gets tremendous laughs is when, after you’ve started having an affair with Jake , you say to your girlfriends: “It turns out I’m a bit of a slut.”

Streep: It’s because I’m saying, “We’re not done, baby! Don’t underestimate me.” Why are we consigned to the rubbish heap at a certain age?

Then there’s the other line, which I can’t imagine most people ever thought they would hear Meryl Streep utter: “Yes, I like a lot of sperm.”

Streep: “Semen”, I believe.

Do you think people are going to be surprised to see you doing nude scenes at this stage in your career?

Streep: Nude scenes?

Well, the hint of…

Streep: Sex scenes, love scenes. Yes, at this age it’s unusual for somebody to do a love scene, to be making love. Yeah, that is unusual. But that is just how benighted we are. Because, you know, we still are alive. It’s you and I, baby. It’s authentic. The whole idea that you have to look a certain way and be a certain age to earn love is ridiculous. We love what we love. It doesn’t matter what shape it is. It’s thrilling to see real people on screen. The thing that broke that little barrier for me was Julie & Julia, where everyone said, “Isn’t it remarkable that a tall overweight woman and a short bald man could be in love?” Well, yeah? You know what I mean? You’re alive.

Baldwin [mock angry]: And the day you brought Stanley Tucci to the set of our film, I hated you for doing that. I thought, what a rude thing of you to do.

Streep: Did you really?

Baldwin: I was soooo hurt that you did that, because you and he had such chemistry. You were lovely together. It was like bringing your ex-husband to the set.

Streep: Oh, my God, I never thought of that.

Baldwin: Obviously you didn’t! I was your man in this movie, and you brought Stanley there? My penis telescoped up into my body. You know what? I’m going to do one of those movies like 300, where I’m all muscled up, and I’ve got my boobs all oiled and everything.

Streep: And they’ll be going, “Alec Baldwin’s back! He’s back!”

Baldwin: But do you know what they’ll say? “It’s digitised, it’s not even his body, it’s CGI.” It doesn’t matter what you do. That’s what I’m telling people about this movie. When you see me take my shirt off, and I look like I have a big gut in that scene, it’s digitised. Because, in real life, I’m so damn muscular.

Streep: A guy told me yesterday that James Cameron said, “With what I can do now” – with CGI or whatever the hell he calls this thing, motion capture? – “I can have Meryl Streep play Abraham Lincoln.” And I thought, I can go on for ever. Actually, we kind of resemble each other. But I’d have to wear those tall shoes again.

Both of you could sell the rights to your future digitisation. Streep: And you’d better do it now, because if you don’t, your children will sell it. They’ll sell it so fast, they’ll sell it to sell vacuum cleaners.

Baldwin: But I’ll only allow them to show me on screen if my pecs are oiled and my abs are tight and my buttocks are clenched and I have a sword in my hand.

Streep [mishearing]: Your buttocks enlarged?

Baldwin: My buttocks clenched, tight, like rocks.

What is most important about your characters in It’s Complicated?

Baldwin: Jake is not a guy who wants to have a fling with his ex-wife because he’s bored. This is a man who is still in love with his ex-wife. My job on this movie was to make her – Meryl’s character – feel loved, because my character is in love with her. He married somebody else and he made a mistake, and now he wants to come back.

Streep: For me, it was just to let myself be pulled, pulled, pulled into it – even though I knew it was bad for me – and try to not get lost.

Baldwin: I don’t think Jane is primed to even let Jake in until she finds she has feelings for another guy. She’s ready to be with someone, it’s been 10 years, but when she sees him, she panics and she goes back to someone she knows.

Streep: That’s the smartest thing you ever said, and, by the way, from now on I’m saying that was my motivation, even if it wasn’t.

Baldwin: I have spoken to a lot of men about this. You are lying there in bed in the last desiccated, arid months of your bad marriage. You’re lying there hoping a meteor hits that house and kills everybody in it. You can’t take another night of the tumbleweeds blowing through the bedroom, and you can’t eat another pint of ice cream and watch late-night news shows. You fantasise about a woman you want to be with. And Jake is a guy who goes out and meets and marries that woman. But by the time you have gotten out of the one marriage, gone out on your own, identified and seduced and married the other woman, a few years have gone by. All of a sudden, you’re 51 years old and your new wife is 31, and you’ve changed, and you’re thinking, “There are a lot of things about my ex-wife I really miss.” I know a lot of men who are like Jake. They think they want a certain thing, but by the time they get it, they’ve changed and they don’t really want it. They want…

Streep: …They want to go home. It’s all about going home. And the longing to make that right.

Baldwin: When I was a kid, my dad watched the news every night. And I would watch the news with my dad. When I was about 10 years old, I remember Jean Harris killed her boyfriend, Dr Tarnower – the famous Scarsdale murder trial. They were talking about the case on the news, and my dad, who never talked about relationships, put down the paper and looks at me and he goes, “These are the things people kill each other over.” And, you know, he was so right. You can make millions of dollars, you can get awards and prizes, you can have the world at your feet, but this is the part of our lives that really destroys a lot of people. They are unhappy. They make bad choices. It’s Complicated is about that. Well, the comedy version of it.

You’ve had your own taste of that.

Baldwin: I was divorced, and that was tough. Nobody sets out to get divorced. Now, when I see my friends and I see the husband do something, I lean in and say, “If you don’t want to end up like me, don’t do that. Don’t pick a battle.”

Streep: Yeah, don’t sweat the small stuff, right. In a long marriage, my God. You’ve got the cabooses [guard’s vans] so far behind the train.

As you watch your children growing up, what do you wish you had known at their age?

Streep: That I didn’t have to do anything I didn’t want to. You have a responsibility only to your own integrity. Other people say, “You have to pose for this and you have to go on this cover.” No, you don’t. You just have to do the work. The work sustains.

Do you find it surprising that you’re getting such terrific roles at this stage in your career?

Baldwin: Jesus, it’s true. It’s a great time for you. And that f***ing Stanley Tucci. Sorry.

Streep: It shouldn’t be unusual. I mean, what character that I have played in my life is more important than any other character? Are the young ones more important than the old ones? Are the fat ones more important than the thin ones? Are the dark-haired ones more important than the blonde ones? What are we talking about? These are people. These are lives.

Baldwin: I’m going to say something, and I’m sorry if you don’t like it, because I don’t get opportunities like this. You know what made Brando Brando? He put the pieces together when he was young. This is a woman, she put the pieces together from day one – The Deer Hunter, The Seduction of Joe Tynan, Kramer vs Kramer. Likeable, unlikeable, she played the role. What’s amazing to me is that you see all the way down, from back then to Julie & Julia – and what we did in this film – she doesn’t lose her vulnerability. There’s a thing in her face, there’s a thing in her eyes, a thing in her voice. A lot of actors aren’t like that. They can’t go there as they get older, they really can’t access that in themselves any more.

You know what? I think it’s the martinis. A good martini is what keeps Meryl Streep fresh and alive.

Streep: What’s this interview for?

The Sunday Times of London.

Streep [shocked]: I think I’ll kill myself.

It’s Complicated opens on January 8