At the end of every performance of her one-woman show I’m Not as Well as I Thought I Was, Ruby Wax sits in a chair at the front of the stage and invites questions from the audience. Hands shoot up. People are desperate to talk to her.

A woman in the stalls asks her how she copes when she’s in the grip of depression. “I do mindfulness meditation,” Wax replies. “But when you get ill, you get ill. It [depression] doesn’t care what you’re doing.”

So, how are you feeling right now? the woman asks, as if talking to a friend over coffee. “I’m OK, genuinely,” Wax says, her Midwestern accent unblunted by all the years spent living in the UK. “But ask me again next week.”

If, like me, you’re old enough to remember Wax as one of television’s punchiest comedians at a time when Back to the Future was still in cinemas, her latter-day incarnation as a mental health activist, author and lecturer can be a little disorientating. She’s still funny, of course; wickedly so. But these days her comedy has a purpose. By laying bare her lifelong battles with depression, her stints in psychiatric institutions and the treatments she’s undertaken, she seeks to engage, educate and de-stigmatise as well as entertain.

In I’m Not as Well as I Thought I Was, we find her embarking on a globetrotting search for enlightenment. She attends a 30-day silent meditation retreat in California, swims with humpback whales in the Dominican Republic and works at a refugee camp in Greece. Each experience yields plenty of laughs, but moments of revelation too. The adventure is curtailed when she joins a Christian community in Yorkshire, realises her depression has returned for the first time in 12 years and admits herself to a clinic.

“I love being in institutions, they’re my happy place,” she says when we meet in the small, overheated dressing room of the London theatre where she’s performing I’m Not as Well as I Thought I Was. “You’re not happy when you admit yourself, but after a while you start to fit in. People tell unbelievable stories and you don’t want to leave. It’s too much fun.” She pauses then says, “I wouldn’t expect people to think this is normal.”

Today, she’s wearing a smart tweed jacket over jeans and white sneakers. She wouldn’t usually wear the jacket, she says, but Monica Lewinsky is coming to tonight’s show and Wax wanted to make an effort.

She’s 71, but her age isn’t something she discusses. “I just don’t like to be pegged,” she says. “I don’t talk about being a female or white either. Those aren’t my specialities.” One gets the impression she doesn’t suffer fools gladly and worries very little about saying the “right thing”.

The kohl-lined eyes study you with a forensic intensity and she gives blunt, succinct answers to questions as if conserving her energy. When I ask how she describes herself these days, she says, “I have no identity. Clearly, I’m a performer when I’m onstage, but when I come off, I’m not a performer. There’s just ... nothing.”

I wouldn’t expect people to think this is normal.

I wait for the punchline, but it doesn’t come. “Wherever I go I think that’s where I live,” she continues. “That isn’t a lie. I forget I have a family sometimes. It’s bizarre. People have to remind me that I have three kids and a husband [she’s married to British film and TV producer Ed Bye]. I don’t have sentimental feelings about anything. If my house burned down I’d go ‘big deal’. I’ve always felt that way. I don’t think it’s related to depression, it’s just the feeling of never having a home.”

I must look a little startled at this point because she switches the dial. The lipstick-coated lips curl into a toothy smile.

When she first arrived on the scene, Wax appeared a straightforward proposition: she was the crude, loudmouthed Yank who became one of British television’s brightest comedy stars of the 1980s and 1990s. In 1985’s Girls on Top – a sitcom developed as the female version of The Young Ones – she held her own in the company of three other nascent stars: Dawn French, Jennifer Saunders and Tracey Ullman.

Moving to the BBC in 1991, she made a name for herself as a no-holds-barred interviewer of the rich and famous. In two series of Ruby Wax Meets … she cajoled everyone from Madonna and Tom Hanks to Imelda Marcos and O.J. Simpson into revealing something of their true selves. In an era before social media, when celebrities still seemed unknowable, these anarchic, uproarious encounters became must-see television. When things went badly – her tense encounter with Donald Trump still makes difficult viewing – it only burnished her credentials as a tough cookie.

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The reality, of course, was far more complicated. She was born Ruby Wachs, the daughter of Austrian Jews who fled the Nazis in 1938 and settled in Evanston, Illinois. Her childhood was a battleground.

In I’m Not as Well as I Thought I Was she recalls how her parents criticised every aspect of her appearance and wondered aloud who would marry their misbegotten daughter. Occasionally, the insults spilled over into physical violence.

“They got a wild child and they wanted to tame me,” says Wax. “But I wasn’t wild in a sexual way, I just hated them. So I’d do things to spite them like hitchhiking rides on private aeroplanes. I wanted to have fun and go with people they found disgusting. And they always found everyone I chose disgusting.”

Years later, a therapist suggested Wax’s depression was the result of trauma; that her childhood had given her PTSD. Both her parents are dead now and there was no reconciliation. “We never had that scene at the end of the movie where you hug and say you’re sorry.” Has she forgiven them? “It’s not an issue. They died. I don’t know who they were, so I can’t comment.”

Wax moved to the UK to study drama and put an ocean between herself and her parents. After being rejected by RADA several times, she got a place at the Royal Scottish Academy of Music and Drama. “Nobody wanted to live in Glasgow at the time, it was like an ashtray with traffic lights,” she recalls. “They only took me ’cos I could pay for it.”

Vindication came later when she won a place at the Royal Shakespeare Company, an achievement she still lists as her proudest moment. “I did Antigone for my audition because I can do hysteria like nobody else,” she recalls. “Any Greek tragedy is like a sitcom for me.” During her six years at the RSC she began writing comedy shows which were directed by Alan Rickman, her flatmate and best friend. “I’d cast all these [RSC] stars as my handmaidens,” she recalls. “Zoe Wanamaker, David Suchet, Richard Griffiths, Jonathan Pryce … people who became quite famous. They’d play smaller parts, and I’d be the lead.”

The working relationship with Rickman lasted almost 40 years, and his death in 2016 devastated her. “I made him laugh, and he made me think,” she says. “If I could make him laugh it was a triumph. In fact, the only reason I went into comedy was to make Alan laugh.”

She’s looking forward to touring her show in Australia, partly one assumes because it will provide the forward momentum that helps maintain her equilibrium. But she’s also excited about seeing the cabaret performer Melissa Madden Gray (aka Meow Meow), a close friend she was introduced to in London by Kathy Lette.

Like many members of her audience, I feel compelled to ask her if she’s OK. “This week I am,” she says. “But when I don’t have anything to do I’m miserable. I know I have to write another book, but I can’t think about what to write about. So that’s disturbing.”

She takes a sip of tea and the room falls silent.

Ruby Wax performs I’m Not as Well as I Thought I Was at the Adelaide Fringe Festival, March 22-23, the Canberra Comedy Festival, March 27, and Melbourne International Comedy Festival, March 29 and 30, and in Sydney, April 10.