The house I grew up in was filled with the ghosts of Soviet tyranny. Nikita Khrushchev was a neighbour when my parents moved in, Vyacheslav Molotov still living there when I was born. The petrol bombs that bear Molotov's name may have granted him an unwanted immortality, but to us he was just another old man shuffling through the entrance.

The building was an apartment block close to the Kremlin and reserved for the leaders of the nation. It was grand and pink and fin-de-siècle, but even here the facilities were basic. The wires were pinned on to the wallpaper and when I was born, cooking was still done on a stove in the corner.

On the third floor a man in a grey suit was always waiting, smoking cigarettes and watching everybody. We assumed he was KGB. Years later, when the Soviet system finally collapsed, we found out we were probably right. All our rooms, we were told, were bugged.

My parents were young when they had me in 1980, students in their early 20s, but we lived in the heart of Moscow's power elite because my maternal grandfather was a distinguished scientist. He was the head of biology in the Soviet Academy of Sciences, which basically meant he ran biology across the entire country.

Under communism, that got you selected alongside party bosses and generals as somebody deserving a truly prestigious home, and No 3 Romanov Lane was nothing if not prestigious. The house was so packed with the shades of Russian and Soviet history that it takes centre stage in Molotov's Magic Lantern by Rachel Polonsky, one of the best books on Russia to come out in years. At its front were huge granite slabs memorialising the revered people who had lived there, the Soviet equivalent of blue plaques. The contrast between these leaders of the past and the Soviet elite of my era could not have been more striking.

I remember the shortages and the empty shelves. My mother and I would queue for hours for the most basic goods – one Soviet skill that proved useful when we ultimately moved to Britain. It was well into the 80s before my father managed to get his hands on a car. It was a Lada, and it broke down all the time. One year, on a trip to Volgograd – or Stalingrad as it was previously known – we were left stranded when it took days for a new part to arrive.

Like so many families in the Soviet Union, we had a strange and divided relationship with communism. My mother's grandfather was a senior official during the war, controlling food supplies and organising the evacuation of his ministry to the east when Moscow was threatened by the Nazis.

He had power and prestige, but with that came the fear faced by any high-ranking official of the period. People he worked with were sent to the labour camps for arriving only a few minutes late for work, or for not being able to immediately provide the exact information from memory that a more senior party official demanded. One time he discovered money had been taken from a safe at work. He was so terrified of what might happen were news to get out that he used his own money to cover up the loss, paying people's wages out of his own meagre savings.

In 1952 his superior, Anastas Mikoyan, probably the most likable of Stalin's blood-drenched cronies, fell out of favour and was lambasted at the party congress. If there had been a purge, my great-grandfather would probably have found himself on a death list. To his dying day he was certain that only Stalin's death five months later saved him, and he remained too terrified to talk about the period: my father would try to ask questions and he would wave him away, pointing to the corners of the room in case those listening heard and came to take his family.

Lebedev's great-grandfather remained convinced that only the death of Stalin in 1953 saved his life

Despite this, both my grandmothers were strongly in favour of communism. They still are. I can see why the promise of "from each according to their ability, to each according to their need" appeals, but what surprises me is how even now they believe in Stalin. Both talk with pride about how they wept at the news of his death. It is not that they do not know what happened under his rule: the famine, the camps, the fear. But they maintain Stalin did not know what was going on. Mistakes were made and things got out of hand, but the Great Leader was not to blame.

This is not an uncommon view in Russia, but I find it difficult to understand how two such worldly wise people can cling to such a belief. Maybe it is simply a desire for the stability and security communism promisedBoth were certainly vocal during my childhood that the only alternative was anarchy.

By the time I was born, my father, Alexander, no longer believed in communism. Around our apartment were hidden the forbidden books of Alexander Solzhenitsyn. He saw the state the country was in and quite rightly blamed the system. Yet these doubts did not stop him from starting work in the foreign intelligence service after he graduated, even though it was a decision that many in our family disapproved of. He immediately established a reputation as one of the sharpest brains in his cadre, with a prodigious memory and eye for detail.

His father had never joined the Communist party as he disapproved of the perks and special access to food it provided to its members. His career as a brilliant optical engineer stalled as a result. Even my maternal grandfather disapproved, despite his work for the Soviet state. He saw foreign intelligence as the descendant of the monstrous organ of internal repression he had so feared in his youth, although by the 1980s foreign and domestic intelligence were operationally separate.

Nevertheless, for a young and ambitious man like my father, the service was an attractive proposition. He saw it as an opportunity to travel, to progress, and even to argue for change from within.

As a child, I did not know what his real job was. The official story was that he was a diplomat and I had no reason to doubt it. I only discovered the truth when I was 11 and found some medals in a drawer, awarded for service to his country. I was sworn to secrecy, but carried the secret with pride. I was still a boy and the idea was exciting; glamorous, even. In a land of grey bureaucrats, my father was someone special.

My first school was an elite kindergarten in Moscow. Soviet child-rearing was not like the western-liberal style: you were ordered to do gymnastics, to sleep in the afternoon, to eat everything they put in front of you, however unpalatable it might have been. Once I fell over and burst my nose open. I knew it was a bad idea to ask the nursery staff for help – there would be little sympathy there – so I ran off into the forest and hid.

My first holiday was to the radioactive wasteland of Chernobyl. In 1989, three years after the meltdown, my grandfather was researching how radiation had affected animal life in the area, and he took me along. I remember abandoned vehicles everywhere, and these gigantic distended mushrooms. We shot a duck on a lake and checked it with a Geiger counter. The readings were normal so we built a fire, cooked and ate it.

My father was posted to the London embassy when I was eight. At 29 he was incredibly young to get such a prestigious job, although the reality of his daily work was less glamorous than I imagined. He was mostly stuck in an office reading the newspapers, occasionally meeting people, and then writing home about what was going on.

Arriving in Britain was a shock. Everything was so colourful: the way people dressed, the cars, the range of goods in the shops. With the freedom to speak, freedom to purchase and freedom to travel it seemed like another planet and I immediately loved it. In fact, I loved everything about Britain, even the weather. It is a beautiful mixture – and when the sun comes out, British people really appreciate it.

Tanks in Red Square during the abortive anti-Gorbachev coup of 1991. Photograph: Dima Tanin/AFP

Every summer, we went back to Russia and I was on one of these holidays the summer the Soviet Union collapsed. I can remember taking our Siberian husky for a walk when tanks rolled down the street past our apartment and parked by the Kremlin. Then, one night shortly afterwards, we were returning from seeing my paternal grandmother when a curfew was imposed. We were on the Moscow metro and people began to be ushered out and the stations closed. When we reached street level there were units of soldiers patrolling the streets with machine guns. This was the night of the attempted coup against Mikhail Gorbachev, when the old guard made one last ditch attempt to reverse his reforms.

My grandmother was very much in favour of the coup. She wanted to save the Soviet Union at any cost. Her husband, my grandfather, said that if they started bashing communists, our house would be the first to be attacked because it was full of Soviet officials, military commanders and party leaders. One night people came and daubed swastikas by the entrance and from then on I found myself looking over my shoulder as I approached the front door.

My parents, however, were against the coup. They went to protests at the White House, where the Supreme Soviet met, when Muscovites gathered to make clear there could be no going back. Stuck to the walls of the metro stations were Boris Yeltsin "Wanted" posters. These provoked a fierce argument back at our apartment between my father and maternal grandmother. He said Yeltsin was a patriot; she thought him a criminal threatening the state she had served her whole life.

We had to return to London before the crisis was over and it was a year before we visited again. By then the USSR had dissolved and even to a child it was clear how much things had changed. Moscow was not the same city; the recent past was being removed from sight. Street names had changed. Landmarks vanished. Historic sites were being demolished and replaced by monstrous new buildings. It is a very Russian propensity, the desire to wipe the past clean and start from scratch. They did it in 1917; they did it again, to a lesser degree, in 1991. Everything people knew was turned upside down.

Muscovites in Red Square celebrate the failure of the hardline communist coup in 1991, signalling the dawn of a strange and wild new Russia. Photograph: AFP/Getty Images

Russia had become a wild place. You heard about death everywhere. People were being stripped at gunpoint just for their clothes. My grandfather started carrying a second world war pistol inside his jacket. At weekends we went to the country and he taught me how to use it, just in case.

Before, people had thin wooden doors, and apartment blocks were left open. Now giant iron doors appeared everywhere. Bullet-proof. Double-skinned. Steel. And people were behaving so strangely. Everywhere that was not locked up started to literally fill up with shit. People used to just shit and piss in every available space. You would even see it in lifts, or in apartment lobbies that had been left unlocked.

I can imagine why the East Germans or Czechs would have felt overjoyed at the collapse of communism, but in Russia it was different. It had been a superpower and Russians are proud people. They were proud to be living in a country that could stand up to America, which others were scared of. Then suddenly, it just fell apart. My maternal grandmother made no secret of the fact that she believed herself totally vindicated, and that all her most dire predictions had come to pass.

My father resigned from government service and started launching business enterprises. He tried everything. He was hungry to try all the things he had not been allowed to do under communism – to buy and sell. He loved the process. He wanted to take all the great things he has seen in the west and try them in Russia. I remember he started selling shoes; one time the consignment went wrong and we had thousands and thousands of left shoes. But he was doing well. Soon he had a new car, a driver and security. He knew how dangerous it was. In Moscow in the 1990s, people were settling business deals not by doing a better job than their competitors, but by killing them. It would be as if Tesco, instead of competing on price or service, just had everyone in Sainsbury's arrested, or shot.

It was 1997 when I first felt the chaos intrude into my own family. I had asked to go to boarding school in Britain but I came back in the holidays and that was when I realised we were now in danger too, for my father was called in for questioning by the police. He knew exactly what had happened. His business rivals had bribed senior officials to go after him and shut him down. It happened, he told me, all the time. That did not stop the police arriving shortly afterwards at my grandfather's apartment. They tore it apart as my mother and I stood there, watching.

That was only the start. Sometime later, behind my father's chair at work, we found a bullet in the wall. It had been fired from an apartment across the street. Another time, we received a tip-off of an assassination attempt. A search was conducted of the surrounding buildings and a rocket-propelled grenade launcher found by a nearby window.

My father refused to leave. He had seen free countries and refused to accept that the same was not achievable in Russia. He started using his money to fund a free press – especially Novaya Gazeta, the freest and bravest newspaper in Russia, where journalists are murdered with horrifying frequency, simply for telling the truth. All this time the police were harassing us, endlessly questioning my father.

Even now my father refuses to back down, without concern for the personal or professional cost, when he sees injustice, corruption and other abuses. I respect him for that. He is a patriot and that is why he believes his country deserves to be better than it is.

I am also a patriot. Russia is the land of my birth and I am proud of it. I wish to do all I can to help it take its rightful place as one of the world's leading nations, not only economically or militarily, but culturally and politically too. Nevertheless I now live primarily in Britain and my British side helps put into perspective the challenges it now faces. Living in a free, liberal and open country with due process and the rule of law throws the present injustices that exist in Russia into sharp relief.

As for my Russian side, the side that grew up in a bugged apartment a stone's throw from the Kremlin, that shows me how lightly British freedoms are taken by the people of this country. It sets off alarm bells when I see the state impede civil liberties, or when technological advances and unethical behaviour threaten our privacy in ways far more sophisticated than the KGB could ever have conceived.

It is because of this sense of how fragile these freedoms are that I am involved in the Independent, the Evening Standard and the Journalism Foundation, which supports and promotes free and independent journalism throughout the world. When you argue for freedom in Britain today, it can sound obvious, even banal. But I grew up in one of the least free places in the world at a time when it ruled a quarter of the globe. Freedom is never banal to me. That is why I hope these organisations can help protect freedoms in one of my countries – and help promote a stronger, healthier and more outward-facing society in the other. I feel optimistic.

• Evgeny Lebedev is the owner of the London Evening Standard and The Independent newspaper titles, and editor-in-chief of independentvoices.com