It was 1967, the summer of love, and I was going to get married. But I needed my father, Leonard, to give permission because I was under 21. I hadn't seen him since I was four, when he left my mother, Joyce, and disappeared from my life. I knew he was living in Australia with his second wife, and I nervously wrote to tell him of our plans. He didn't reply.

However, a few months later I received congratulations cards and cheques from two people I had never heard of – Laura and Harry. My mother told me they were my aunt and uncle, my father's sister and brother. But where had they been all my life? She hesitated before saying: "When your father and I separated, he asked me not to contact his family … He was in a terrible state, so I promised."

I arranged to visit my aunt Laura at her home in Essex. We sat in her front room drinking tea and I felt I was being examined, but for signs of what, I had no idea. She told me that the last time she'd seen me was in 1949, when I was three. She said what a pity it was that we'd moved so far away, and asked when my mother and I had come back to England.

What did she mean? Come back from where?

"From Australia, of course."

I stared at her. Neither my mother nor I had ever set foot outside Europe.

"But," she said, "you wrote to your grandfather, and Joyce sent photos." She fetched a framed photo.

The picture was of a girl of about 15 standing by a gate, her eyes hidden by glasses. I wore glasses, too. She was slim, with straight hair, like me. Could that girl be me? Had I been there, wherever it was, and been photographed and then forgotten all about it? Laura didn't seem to doubt that I was that girl, and yet the photo was sent from Australia.

"I don't think that's me," I said with more conviction than I felt.

Laura frowned. "Wait here." She left and returned a few moments later with a shoebox stuffed with envelopes. She produced another photo. "And this isn't your brother and sister?"

"I'm an only child," I told her.

Laura spoke quietly. "I could never understand why your mum didn't write, and when she finally did, the handwriting didn't look right. I told Harry and Father, that's not Joyce's handwriting, but they said I was imagining things."

I gave her the bare facts concerning the past 17 years of my life: after my parents separated, my mother and I lived in a series of boarding schools where she taught, before settling in Exeter, where she remarried.

I went to Bristol University, married straight after my finals and was now a trainee teacher. I hadn't seen my father since I was four.

I thought back to the day he said goodbye. We were at a busy railway station. Daddy lifted me up on to the train and as it started to move, he ran along the platform. I leaned out of the carriage window shouting goodbye and waving until he disappeared in a cloud of steam. I was told that Daddy would be going to Scotland, where he was looking for a house for us to live in.

But at Christmas we didn't go to Scotland. It was then that my mother told me there would be no house there. I was devastated, furious, and I hit out. My daddy had lied, and so had she. As soon as I could write my own letters, I wrote to my father weekly. I'd ask: "When can I see you again?" He would reply: "When you're old enough."

A moment came, when I was about 14, that should have made me give up this quest to see him. I was at home on my own and bored. Rummaging around, I found a letter, and recognised my father's writing. I knew I shouldn't look at someone else's letters but … I took one and began to read: "I think it would be best if you told Susan I was dead." If I thought he was dead, I'd not ask to see him again. He would no longer be bothered by my letters and he could pretend I was dead, too.

Just as I had never told my mother I'd read my father's cowardly letter, I didn't tell my aunt Laura about it now.

Laura then revealed that, before he left for Australia, Daddy said if my grandfather wanted to say goodbye to us all, he could come down to Tilbury on a certain date when the ship would sail. Laura went with my grandfather, but at Tilbury they were told that the ship had sailed the previous week. She had assumed it was an innocent mistake, but now we saw what it really was: a deliberate deception, to stop his father and sister finding out that he was abandoning his family.

That first meeting with my aunt was the beginning of a journey that would take decades, and span thousands of miles. I gradually uncovered evidence of a tangled web of deception and obfuscation created by my father and the woman he took with him from the UK to Australia and who was at the heart of my parents' marriage breakdown.

I plied my mother with questions and she told me more. When Leonard was in hospital during the second world war he befriended a young nurse, Elizabeth. He and my mother were engaged at this point, so my mother got to know Elizabeth when she visited my father.

They lost touch after the war but then my father was offered a job in Birmingham, where Elizabeth was living. She became a frequent visitor at my parents' flat. All three of them were close, and when my mother and the – seemingly single – Elizabeth became pregnant at the same time, Elizabeth confided that the father of her baby was a doctor who was dying.

My mother believed her, but she hadn't reckoned that by the time she got back from hospital with me, she would find Elizabeth and her baby installed in our house. They stayed for several months, so there was a household with two women, two baby girls – me and Sarah – and my father.

"So the photo of the girl was of Sarah, not me?"

"Yes," my mother said. "She's five weeks older than you and her father was Leonard – the doctor was a fabrication. You are half-sisters."

I was incredulous. My father had had a secret love-child at the same time I was conceived, and covertly moved his mistress and this other child into the house he shared with his wife. It wasn't until 11 years later that my mother learned from a friend of his that Leonard was Sarah's father.

I discovered all of this at 21, and was overwhelmed with confusion, and a never-ending series of questions sprang to mind. I was intensely curious about Sarah, and three years later, I met her. She and her husband were living in England. Sarah had only been told of my existence just before she left Australia. Meeting her was a powerful but surreal experience. I think we were both struggling to assimilate the news that the other existed.

Speaking to her, it was amazing to observe not just the similarities between us, but the extent to which our childhoods had mirrored each other's. As a girl, my favourite dolls were a black "mammy" doll and a soft-rope corn dolly. I treasured them: my father had brought them back for me from a trip to America. So it came as a shock to discover that Sarah had been given just the same dolls. It was as if we were interchangeable.

Despite all that I'd found out, I didn't give up on my father. I continued to write and sent photos of my children.

In 1973, I heard that he was in the UK, so I wrote to him again. Would he like to meet us? He was ill, and wanted to go back to Australia. He replied: "I am anxious that you and your children should have every possible happiness. Whether our meeting would add to that happiness I do not know. I have just learned what breaking old physical scars can mean. Emotional scars may perhaps contain just as much a threat if disturbed." He signed off, with "very much real, if distant love".

I felt powerless and cross with myself. At 27, I was no more able to deal with his rejection than I had been at seven. "When you're old enough," he used to write. Would I ever be old enough? Would he?

It wasn't until 1989, nearly 40 years after I had last seen my father, that we met again. I was in Australia and determined to speak to him.

As I stood outside his house, I began to doubt what I was doing. What right did I have to disturb a sick old man and his wife? But I rallied. There are things that need to be said, I told myself, explanations to be made.

In an unexpected – although, given her talent for fabrication, not unprecedented – twist, my stepmother Elizabeth Jolley, the woman he had run off to Australia with, had become a highly acclaimed author. So the face of the woman who opened the door was familiar from the covers of paperbacks.

She ushered me into his room. He lay on a bed, his thin frame propped up on pillows and, despite the heat, a red tartan travelling rug pulled up over his knees. I don't remember any words that were said, just the dizzying sensation of looking into his eyes, which was like looking into my own eyes.

I'd hoped for a grown-up, rational conversation. But when it came to the moment, it all vanished like smoke. Leonard said very little, I found myself burbling on about trivia and Elizabeth hardly allowed me a moment with him on his own. I felt outmanoeuvred.

But then that evening she rang me and said she knew there were things I wanted to talk about and the next time we met I should say whatever I wished.

Two days later I returned, this time with my daughter, who was lively and sociable. She and Elizabeth did most of the talking while I was almost as quiet as my father. At many points I thought, "Go on, say those things you wanted to say, you'll never get another chance." But when I tried to form the sentences, the words stuck in my throat. And despite what she'd said on the phone, Elizabeth made no attempt to encourage me to enter that territory. I was very English, polite and restrained. I kissed them both goodbye, and as we left the room, Leonard looked up and gave an unexpected sweet smile.

I had failed. On the flight home, I told myself I would go back one day, ask those simple, but impossibly difficult questions: why did you lie? How could you plan so much deceit, for all those years? And the most difficult question of all: how much of it was you, Leonard, and how much your wife?

I'd never see my father again. My mother died in 1993, and Leonard a year later. After my mother's death, my aunt gave me a stash of letters sent to her and my grandfather from my father and Elizabeth. Among them were the letters written in Elizabeth's handwriting but signed by "Susan" and "Joyce". I had known about them for years, but seeing them brought back the distress I'd felt when Laura first presented me with the fictitious version of my life from four to 21.

More evidence appeared. When helping my stepfather go through my mother's clothes, I found a packet of negatives shoved at the back of a drawer. I developed the photos myself, and stood transfixed in the darkroom, as long-lost images of Leonard, Joyce and Elizabeth in a garden with two babies emerged.

There was Leonard, with both babies, one in each arm. Standing awkwardly in his long shorts, he looked at neither child but at the photographer. What must it have felt like, to hold your two daughters even as you had to hide the fact that one of them was your child? What could have been going on in his head?

Finally, I was given access to the correspondence between Elizabeth and my father from 1945, when she and my mother became pregnant, until 1950 when he left us. The letters were passionate and at times rather embarrassing. I felt uncomfortable reading them. What came through, though, was the fantastic attraction these two had for one another. His leaving us was inevitable. How sad, though, that he hadn't been straight with his family, with my mother and with me and his other children.

I've come to the conclusion that his was not a coldly deliberate decision to deceive, but that one thing led to another, the lies accumulated and, like a car slithering down an icy hill, the story ran out of control. It's a story that has taken me many years to uncover, but finally telling the truth has helped me to come to terms with the fictions that defined my past.

• A BBC Radio 4 drama based on Susan Swingler's The House of Fiction will air on 4 June