While Chris Tarrant was preparing for his mother's funeral in 2012, her house was burgled. She had been so house-proud that it broke his heart to see the windows smashed and footmarks all over her immaculate worktops. "I felt that everything in my parents' world had been defiled. But one positive thing came out of it. The burglars had ripped open Dad's beautiful old desk, which he had kept locked for as long as I can remember. And as I sorted through it, I spotted an old diary, dating back to 1944. For the first time, I had his own record of his wartime experiences."

Tarrant had always enjoyed a special bond with his father, Basil. "Dad was my closest friend," he says. "We had a similar outlook and I could talk to him about anything. Sex, relationships … whatever." He looks a little sad. "The only thing that was taboo was the war. It was a generational thing. The ones like Dad, who had been in the thick of the fighting, rarely said a word about it. From childhood, I knew better than to ask. But after he died, I realised I barely knew him at all."

Tarrant, 67, is chatting at his publishers in London. Dressed in a sober suit, he seems less blokey than of old and more reflective, though that's hardly surprising. Last month, on a flight from Bangkok to London, he suffered a mini-stroke and nearly died.

Thanks to intensive physiotherapy, his speech and movement are almost fully restored, though his specialist has warned him that his piano-playing days are over. "But that's OK," he quips. "I couldn't play the piano in the first place. The main thing is I've lost a stone and a half in weight. And I get tired. But it's a lesson learned. I'm taking three months off and then I'll decide what to do. Will I go back into television? I don't know."

One thing is certain, however. If his father were alive, he would be among the first he'd turn to for advice. He is never far from his thoughts. Now more so than ever because he has spent the past two years writing a deeply moving memoir about the mysterious war record of his father, who won a Military Cross that was personally authorised by Field Marshall Montgomery.

It was an extraordinary experience, wading through mountains of regimental paperwork and, above all, speaking to the surviving men who had served with his father – men now in their 90s. The revelations astonished him.

Basil joined a territorial unit of the Royal Army Ordnance Corps in 1936 when he was just 17. He was called up in 1939 and went with his unit to France, but was evacuated from Dunkirk in the chaotic retreat in May 1940. But on 6 June, 1944, he was back for D-Day and landed on Juno Beach.

As an officer, he was one of the first ashore, encountering ferocious resistance, but characteristically Basil always made light of D-Day. "He used to say, 'It was all right when we landed, there was just a bit of struggle with the parking.'"

After Normandy, Basil won the MC for leading a night patrol of 16 men through a minefield at Groesbeek on the Dutch-German border, where they attacked two farm buildings housing 60 Germans. Although heavily outnumbered, they flushed out the enemy with grenades, receiving no casualties, before continuing the advance, where the battalion engaged repeatedly with retreating Panzer units.

But perhaps his finest hour came when they pushed on to the German town of Kleve and the scene of Operation Veritable, when, in six weeks, 25,000 Allied and 80,000 German soldiers died. With his senior officers dead, Basil had to take command. "Few of us have heard of the battle, but it was one of the most savage of the whole war," says Tarrant. "It would have been house-to-house, and hand-to-hand, and bayonets."

For his bravery and initiative, his father was recommended for a second Military Cross, but the order was either never received or overruled. "The more I've learned about what he did, the more it rankles," says Tarrant.

Basil's war ended three weeks before peace was declared when his Jeep drove over an anti-tank mine. It was thought he would lose an arm, but surgeons managed to save it. The miracle is he survived the war. Time and again, Basil overcame seemingly insurmountable odds. "He must have learned very quickly how to survive, using a street fighter's intelligence. He also had a lot of luck. He would have seen so many people shot or horrifically wounded."

Listening to the men who served under his father, Tarrant found it hard to equate Basil's heroic and expedient – but nonetheless bloody – actions with the laidback, funny man he knew. "They all said if they had to crawl through a house full of Germans they would rather follow Major Tarrant than anyone else because they thought they had half a chance of coming home. I kept saying, 'You're just saying that because I'm his son,' but they said, 'No, we really liked him. He played football with us. Even though he was an officer, we related to him.'

"Mind you, one chap thought Dad was slightly mad. As they lay behind a wall being picked off by sniper fire, Dad briefly showed his head so they could locate the firing position. The plan worked and they took the sniper out immediately, but they were convinced Dad had been killed. This guy said it was as if Dad had something to prove. He was always in the thick of everything."

Tarrant is immensely proud of his father, but hurt that he felt unable to share his war experiences with him. "I'm sure people will ask why I didn't press harder, but you can't force someone to relive painful memories. He used to go to soldiers' reunions and I reckon that would have been the one time he talked about it."

He also did something he regrets. "I set up my own production company and Dad unexpectedly said, 'I've got an idea for a programme. We could go to Juno Beach, talk about D-Day and the film could go out on 6 June for the 50th anniversary.' I agreed it was a great idea, but there was no way we could make it in time. How stupid was I? Even if the film had never been publicly aired, I should have seized the offer with both hands. Dad was proposing, for the first and only time, to talk about his war experiences and I rejected it. Sometimes in the small hours of the morning, my thoughtlessness comes back to haunt me."

His father died, aged 85, in 2003. "I go to the grave a lot and talk to him. Now, I tell him off. I say, 'Dad, I found this out yesterday – why didn't you tell me?' But I always end by saying, 'I've learned so much more respect, admiration and love for you.'

"When Dad fell ill with heart trouble, we didn't think he was dying because he was tough. But I think he knew because on Armistice Day he struggled out of bed, put on his best suit and medals, and stood to attention in front of the television through the two minutes silence and saluted.

"When they played the Last Post, tears were streaming down his face. And he never cried. Never. He hated people seeing him like that, even when he was in pain. And he said to me, 'Promise me you'll never mock the memory of those men, boy.' I solemnly promised, and of course I never would."