In Arbitrage, you play the wife of a multi-millionaire hedge fund manager who is stronger than she first appears. It's not the usual character arc for a female support role – was that part of the appeal?

Absolutely and I was also taken by Nicholas Jarecki's enthusiasm and passion, and Richard Gere, I've known forever and I got to work with him. I got to wear nice clothes and film in New York, so it was very seductive.

I think that what happens in a long relationship [like the one in the film] – and the longest I've ever had was 23 years – is that people have assumptions and firm habits in the way they relate to each other. He [the Richard Gere character] has made certain assumptions about her but when she gets the upper hand, it makes him reload. She has made certain compromises but she's a smart woman. I liked that.

You're known for playing strong women…

Except I don't particularly think of them as strong. A lot of the women I play may make difficult decisions but when I'm playing them, it doesn't feel strong. I know a lot of people say that about Thelma & Louise but that was a woman on the brink of a nervous breakdown. She did something she had to do. Again, Sister Helen [in Dead Man Walking, for which Sarandon won an Oscar in 1996] didn't come in firing all the big guns at the top of the movie, she incrementally becomes deeper and deeper involved. But in hindsight, they seem like strong women.

Would you call yourself a feminist?

I think of myself as a humanist because I think it's less alienating to people who think of feminism as being a load of strident bitches and because you want everyone to have equal pay, equal rights, education and healthcare.

It's a bit of an old-fashioned word. It's used more in a way to minimise you. My daughter [Eva Amurri, from Sarandon's relationship with Italian film director Franco Amurri] who is 28, doesn't even relate to the word "feminist" and she is definitely in control of her decisions and her body.

You are known for your activism and have been involved with a wide range of campaigns. You famously spoke out about the plight of HIV-positive Haitian refugees at the 1993 Academy Awards and have opposed the Iraq war, supported the Occupy Wall Street movement and highlighted the environmental damage done by fracking. Do you ever think: "I just can't be bothered"?

[Laughs] My heart gets broken often. It's more a question of can you live with yourself if you don't say something, and that gets you through when maybe your energy is low. And it's at the grass-roots level that they're dealing with really difficult stuff. I'm more of a dilettante so I can't really complain.

You are one of those actors people feel they know. You've said before that when you broke up with Tim Robbins, your partner of 23 years, strangers would come up to you in the street and tell you how sad they were. Was that surreal?

Well, everything [about fame] is surreal. That's why I don't take it too seriously. I'm pretty straightforward in interviews and it's too late to start lying now… I think people probably do know me to a certain extent. I've been vocal about my philosophy of life, my mistakes. I never speak specifically of my relationships, probably because I'm a bit superstitious. When Tim and I both decided to split, certainly you feel the pressure not to let people down beyond your immediate family because people have enjoyed what they think of as your perfect relationship. You have to try to dissociate yourself from those demands and that is kind of a weird thing.

On the other hand, people come up to you in the street saying, "I love you" and it's completely unearned also, but it's a very nice way to start the day.

Have you ever felt the name "Susan" doesn't accurately reflect your personality?

You mean it's boring?

No, not boring… just very sweet.

It is kind of boring. It's hard to find a Susan under 35. They should take some of the Jessicas and rename them Susan. There are so many Jessicas around. A lot of people my age who were called Susan changed their name to things like Sigourney. It never occurred to me to change it and then I was re-invented as a Sarandon [when she married actor Chris Sarandon in 1967. The couple later divorced] and I liked that, mostly because my parents weren't very supportive about me wanting to become an actress. But, yeah, it's a little late in the game to start rethinking it. I mean, my daughter isn't threatening to call her children Susan or anything. In fact, I met a girl named after me at the Toronto film festival. I thought her mother was going to say she was called Susan but she said: "This is Sarandon." I was like, "Oh my God. Really?" I even had a picture taken with her.

You're the eldest of nine children. Did that mean you were the sensible, capable one who looked after everyone else?

Definitely and I've continued to be the kind of mother figure. It took me many years to learn how not to approach my romantic relationships in a mothering way, and certainly on set, I end up being the one who does the birthday parties and has everyone to my house for my home-made barbecued chicken.

You're rumoured to be dating a 33-year-old. Have you learned how not to be a mother in your personal relationships now?

Figuring out how to hold on to yourself and where the boundaries are is one of the big lessons that women have to learn because we're conditioned by society to act as producers, not to grab power for power's sake. We know how to make people comfortable, how to finish their sentences. So what is difficult as a woman is to stand up for yourself and hurt people's feelings occasionally.

What is the secret to your home-made barbecue chicken?

Making the barbecue sauce from scratch. When I was doing Bull Durham, I perfected a fabulous barbecue sauce with molasses and a few different things and I made it non-stop…

I'm proud to say my boys [Sarandon has two sons, Jack and Miles, from her relationship with Robbins] can cook. The things I told them to do if they wanted a good woman were to learn to listen and to learn to cook breakfast, lunch and dinner. They can do that. My youngest son is a tremendous baker.

Arbitrage is released on DVD on 15 July