If I ever imagined meeting Australian actor and comedian Magda Szubanski, it wasn’t here: in a plush Chelsea hotel, complete with a silver tea set and a pile of tiny sandwiches. But Szubanski is entirely unaffected, immediately forthcoming and soothingly at ease. “This is all a bit My Fair Lady, isn’t it? I could bloody murder a sarnie,” she announces, before charming the waitress – also a Magda – with a brief but effusive exchange in Polish. “I do have to be careful,” she says afterwards. “I’m too good at accents, so when I speak other languages, people always assume I speak it better than I do.”

That ear for voices and eye for appearances has fuelled Szubanski’s astonishing roll call of iconic performances over 30 years. Perhaps her most famous, certainly overseas, is the ungainly “second best friend” Sharon Strzelecki in Kath & Kim. But before that there was an abundance of sketch-show characters that made her a star in Australian homes: the oblivious chat show host Pixie-Anne Wheatley, lip-pursing saleswoman Chenille, the skinhead Michelle. On the big screen, she was the cuddly farmer’s wife Esme Hoggett in Babe, along with small turns as a maid in The Golden Compass and a penguin in Happy Feet. No matter how tiny the part, it is hard to think of another Australian actor who can spark such joy in an audience. I remember seeing Indigenous Australian musical Bran Nue Dae and hearing a little chorus of pleased hums go up around the cinema at her brief turn as a randy tuckshop owner (“We’ve got hot sausage rolls … ”).

While a varied lot, Szubanski’s characters are united by their guilelessness and often, their grotesqueness. But her willingness to be painfully, hilariously embarrassing sits at odds with the person she reveals in her memoir, Reckoning: someone pursued by anxiety and depression, self-critical, constantly aware of her very being.

Starting with what may be the most tantalising first sentence of any book this year – “If you had met my father you would have never, not for an instant, have thought he was an assassin” – Reckoning, which was published in Australia in 2015, is as much a biography of her father as it is about her. Zbigniew Szubanski is ever present in the book, as a figure of both love and mystery. A Polish Catholic, Zbigniew joined the Polish execution squad, Unit 993/W Revenge Company, aged just 19, killing Gestapo officers and Polish collaborators in Warsaw. His story is a series of incredible close calls: hiding Jews in the family home, escaping the Warsaw Uprising through a sewer, fleeing from the infamous Lamsdorf Death March and finally being liberated by Russian soldiers from a POW camp. He then met Szubanski’s mother in Scotland and moved to Liverpool, where Magda was born in 1961.

How does a Polish assassin end up as a father in Australia, especially one who, according to Szubanski, relished the mundanities of suburbia? Much of Reckoning sees daughter sorting through the puzzle of her father, picking apart moments where they clashed and considering events from before Magda was even born, to come to an understanding about how trauma can be passed from one generation to another. Eight years of writing resulted in an 850-page draft and also what she calls “a reactive depression”, from recalling the worst of her family’s history. “If you don’t dissociate, if you let yourself feel it, it is gonna mess with you,” she says. “I felt the least I could do was witness it and feel it. Some of it was just harrowing. Some of the things my father told me were unbearable, y’know?”

Reckoning never reads like it would have been cathartic to write; Szubanski isn’t sure herself. “If it was, it was the slowest kind of catharsis. It is like if you do yoga every day and it changes you over time. It’s the same thing – you’re using your psychological and emotional and moral muscles as you write. It really changed me.” But she does feel like she now understands her father better. “There was no bitterness in him. I have a real admiration for him and also for the subtlety of his moral philosophy. I think he was very hard on himself. But that is what PTSD is; he lost his belief in his own innocence, his own goodness. Most of us go through life thinking we’re good people and we can afford to because we’ve never been put to the bloody test! But the Poles, the Jews – some of the dilemmas they were forced into are awful. You just have to hope that it never happens in your lifetime.”

The Szubanskis migrated to Australia when Magda was five. A “shy showoff” with a name even she couldn’t pronounce until she was 10, Szubanski’s recollections of feeling like an outsider are painful to read. Clashing with her father, obsessing over the implications of her crush on Marcia Brady, struggling with grades and then her weight. Then a moment of clarity came, in the form of a part in a school production of Salad Days. “I was no longer an outsider flailing on the periphery of life,” she writes. “I was standing at its red-hot centre.”

Even now, she speaks of that moment with reverence, almost like she doesn’t believe it happened herself. “The moment my foot hit that stage, I just felt at home. I felt at ease. And I still do. Maybe not so much as I get older and I forget lines – that’s a whole nightmare of its own.”

Being an outsider gave her a keen eye and ear for what made up being Australian, which helped on shows like Fast Forward and The D-Generation where she often played bogans (Australian louts) – to great effect. “I always felt like I was holding on to Australianness with my fingernails,” she says. “When you are on the outside like that, you can observe while you’re madly trying to understand it. It actually took me quite a long time to feel Australian. And I still don’t, at 55. I am very connected to the European side as well. I don’t think you have to choose – it’s not that if you love one it means you hate the other. The more we can become less tribal and more global, the better.”

In 2012, Szubanski came out as gay on national television, a decision she says felt natural. But the timing was crucial; after years on television and film, crafting some of the most famous characters in Australian comedy, she had become what she calls “a gay sleeper cell” and was somewhat protected from any backlash. “I was at peak fame, so I used it,” she says. “To be honest, I reckon if I came out earlier, it would not have worked so well.”

At one point in Reckoning, she likens her sexuality to being “delayed at takeoff and … stuck on the runway ever since”. Does she still feel like that?

“Probably,” she says, and guffaws through a mouthful of sandwich. “In fits and starts it has taken off. But homophobia really did have an impact on relationships. For people of my generation, it was a trauma.” She now watches younger LGBTQI people holding hands in public or getting married with “a slight sadness – I think, ‘God, what would my life be like if I had had that opportunity’. But while that’s true, it ain’t all sorted yet. I don’t think the damage done by external and internalised homophobia has been processed yet. We’ve gone from a discourse of shame to a discourse of pride, with nothing but a parade to get us through. You don’t undo millennia of shame and persecution overnight.”

Coming out came with a louder political voice: she is fiercely critical of the Australian government and its refusal to allow marriage equality, and is particularly vocal about politicians with controversial views, such as Nationals MP George Christensen, who likened an LGBT education programme in schools to child grooming. “He got a primary vote of 38,000 out of a population of 23m. How the fuck does he get a say? I’ve got more Twitter followers than that,” she scoffs.

These days, Szubanski has just finished filming Ben Elton’s latest film Three Summers and says that while more acting is planned, she’d love to write another book. (“Maybe fiction? We’ll see.”) Szubanski has won an intimidating number of book awards – book of the year and best biography the Australian Book Industry Awards, a NSW Premier’s literary award, a Victorian community history award – and is enjoying the accolades, despite not entirely recognising Reckoning as her own. “It is a little bit like when a dog farts and it looks around like ‘Did I do that?’ I feel like that. ‘Is that me?’” she jokes, before recalling the night she won the two ABIAs. “I was feeling really up myself, and then I suddenly got teary. I had been too caught up in the awards. The book is really about learning to communicate with people in a real way. And that’s the soul-nourishing thing.”

• Reckoning is published by Text in the UK at £12.99 and in Australia at $32.99.