Back in the 1960s, before today’s many Hayleys (like Kiyoko, Williams or Paige, from the worlds of acting, music, bridal wear), there was only one — Hayley Mills, the blonde British darling of Disney films like “Pollyanna” (for which she won an Oscar) and “The Parent Trap” (in which she played twins).

With her fresh-faced good looks and curious accent, Mills became an icon for a generation, eventually graduating to adult roles on screen and stage. And that’s where fans will find her now, starring in “Party Face,” an Off-Broadway comedy that recently opened at NY City Center Stage II.

Written by Isobel Mahon and directed by Amanda Bearse, the play depicts an evening at home with Irish suburbanite Mollie Mae (Gina Costigan), who’s hosting a cozy gathering — until her meddling mum, Carmel (Mills), arrives. Wine flows, generations spar, and family secrets soon come to light.

Mills, 71, recently spoke with Newsday contributor Joseph V. Amodio.

Q: We get a sense of your character from the get-go when you arrive at your daughter’s party early and start taking over. What type are you in real life — do you arrive early, late or on the dot?

A: I never, if I can possibly help it, arrive early. I think that’s appalling. But Carmel has such great intentions to help things go swimmingly. She’s not blessed with great powers of, um, analysis. And she can’t deal when things go awry.

Q: You’ve got an all-female cast, female playwright, female director — it seems well-timed, given the #MeToo movement and all the hashtags and such. Did that come up?

A: Not really. We were too busy worrying about our lines. But it’s healthy for the planet that women are standing up for themselves. Women have so much to offer. I think it’s more challenging for men these days — thinking, “Whoa, who am I supposed to be?” It’s great to see men pushing prams, changing nappies and things. My boys are in their early 40 now. In my day, the men weren’t doing that. Things don’t happen overnight, do they? But the march of change is … ongoing, and it’s wonderful.

Q: You grew up in an acting family. Your parents, and your sister (Juliet Mills, from TV’s “Nanny and the Professor”), were actors. Did you ever want to do anything else?

A: Most of my childhood was spent on a farm in Sussex. I had a pony and a lot of freedom. I wanted to be a show jumper. But when I went to boarding school when I was 10, I loved making people laugh. So I think I probably would’ve staggered into acting. Or, I don’t know, I might’ve just got married and had children.

Q: Do you think it’s tougher for child actors today to keep a level head?

A: It’s very hard. I don’t know how they do it. When I started, there were few children working. I worked for a very family-oriented studio — Walt Disney was the boss. He knew everybody by name. There was no exploitation, no sexual harassment, nothing like that. I was fortunate. Then I went back to school. Life had some extreme contrasts, but because I was young, I accepted it all — one minute I’m in boarding school and can only wash my hair once a week, the next I’m being picked up by a limousine and everyone’s falling over you doing your hair and makeup. And that was that.

Q: I hear your parents didn’t take you out of school so you could attend the Academy Awards.

A: They were concerned it should never go to my head. That’s why I didn’t pick up my little Oscar and wasn’t even told about it until it appeared one day. Nobody made a fuss. It was years before I realized its significance. You have to remember, we didn’t have computers or Google or Wikipedia. You couldn’t look things up and go, “Wow, this is something to have got one of these.”

Q: It’s funny — I just happened to watch “The Parent Trap” recently, on a lark. Hadn’t seen it since I was a kid. It was just as charming as I recalled. Do you get tired of people bringing up the films you did as a child?

A: No, and I’ll tell you why. Because the ones they mention, invariably, are the Disney movies. It takes people back to their childhoods, and to happy experiences — even if they had troubled childhoods, those Disney films made them happy. And that’s what they were designed to do. I feel grateful I’m part of that experience. This may sound corny, but it’s a privilege to have been in those films. It could’ve been somebody else, but it happened to be me. It’s just the way life worked out.