When Ingrid Loyau-Kennett's bus was halted at the scene of the Woolwich attack, she leapt out to offer aid, but instead ended up engaging one suspect in conversation. Here she tells why

Perched on the edge of her sofa at home in west Cornwall, Ingrid Loyau-Kennett is insisting she is not a hero. "I feel like a fraud. I don't think I did something courageous. In the second world war, people would do something like this every day."

The rest of the nation, it seems, disagrees. Last Wednesday afternoon, the 48-year-old, French-born mother of two was returning from a trip to see relatives in France and, having just visited her children in Plumstead, was on her way to Victoria to catch a coach back to Cornwall. As she sat "watching the world go by" with her suitcases on the No 53 bus, it passed through Woolwich on the way to Parliament Square. It was here that she was suddenly forced, as she describes it, to "confront evil". Her remarkable response triggered headlines around the world.

As the bus turned a corner, out of her window on the right-hand side of the lower deck she saw a body lying in the middle of the road and, a few feet away, a car smashed into a lamp post on the pavement. Her "gut instinct" moved her to jump off the bus to offer first-aid assistance for what she believed to be a road traffic accident.

But a few moments later she was being confronted by two men holding a selection of butcher's knives and a gun in their blood-drenched hands.

What she did next led to universal praise, not least from David Cameron, who stood outside 10 Downing Street the following day to salute her courage in refusing to flee or panic and, instead, prevent further injuries being inflicted on the gathering crowd by calmly engaging the men in an extraordinary 10-minute conversation until armed police arrived. The overwhelming consensus is that most people think that if they'd been in her shoes they would have either run for their lives, or cowered, begging the men to be spared.

"I went to the body and started to take his pulse," she says, speaking rapidly in a strong French accent. "But a Caribbean lady kneeling by his side said, 'No, no, no, he's dead.'" I asked if she was sure, and she said 'Yes'."

Loyau-Kennett still felt for a pulse because her first-aid training made her think a severed artery in his arm might have weakened the flow of blood to the wrist. "Then this black guy said to me, 'Don't touch the body. Go away.'"

She looked up and saw a man and "saw right in front of me two bloodied hands, one carrying a revolver and the other a meat cleaver".

Around her, she estimates that 60 to 70 people had gathered at a distance, all watching, some filming with their phones, none offering to help. Meanwhile, the woman sitting by Drummer Rigby's side was stroking his back and, it was later reported, praying for him. The women have since been dubbed the "Woolwich Angels" – another term Loyau-Kennett, a practising Catholic, is eager to reject. "I didn't have any adrenalin at this moment, but I suddenly realised why the car was like that. It was a murder. I knew then I was in a situation here."

Loyau-Kennett says she has had no problems sleeping in the days since, and hasn't really had a chance – a result of the "storm" of international media attention – to dwell on why she did what she did next.

"I stood up and said, 'Why? Why don't you want me to touch the body?'"

The man, staring hard back at her, told her that the victim was a British soldier and that he "killed Muslim people" in other countries.

"I looked at the body and he didn't look like a soldier to me," she says. Rigby was wearing a Help for Heroes T-shirt, although she couldn't tell this at the time. "Instinctively, and through my scout training, I like to keep calm and be respectful. So I thought, OK, let's listen to what he has to say. I tried to engage him in a conversation."

Talk soon moved to the subject of British foreign policy. "I said to him that I'm sorry that this happens in the countries that he was naming – Afghanistan, Iraq, etc – and I agreed with him that it shouldn't happen. He was saying that women and children were being killed just because they are Muslims and they drop their bombs and no one cares. I said: 'I know, it's very sad.' But I said to him: 'Yes, it's happening, but what do you want now?'"

Loyau-Kennett asked if he needed a car or money to help him flee: "But I really didn't want to influence him in any way. 'I want to fight,' he said. 'In London?' I asked. 'Yeah, I want a war in London.' I said he couldn't do that and why didn't he just join a proper army in those countries and kill as many as he wanted there. That would be a bit more useful than just being in London doing this. He told me he wanted to do it in London. I told him the police would arrive soon. 'I don't care,' he said. 'I'm going to fight them and shoot them.'"

What she said next was picked out for particular praise as an inspiring riposte to terrorists: "'OK,' I said. 'Do you know what? It's only you and there are many of us. What do you expect out of that?' 'I don't care,' he said. 'I will have my war here.'"

As the drama and jeopardy intensified, Loyau-Kennett kept one ear open for police sirens, convinced they must be racing to the scene. "But there was nothing," she recalls, her eyebrows bending in frustration. "I was worried that if another British soldier walked by, he might see that and attack him. And I didn't want him to see the police trying to do something. If possible, I wanted him to see nothing. I wanted him focused on me. He was very agitated and pacing back and forth close up to me. He was really upset, as you might be with an electric company because they've sent you a £2,000 bill. He was educated and had good English. I just thought: 'Talk to me, talk to me.'"

Once again, in an effort to fix his attention, she moved the talk back to the topic of British foreign policy. "I listened to him and tried to engage him in debate. I said for British soldiers it was just a job; they are not an ideological army. I said they are only in these countries because of the Americans. I said you should be against the Americans rather than the English. He looked at me and said: 'That's right. That's a good idea.'"

Loyau-Kennett says she noticed at this point how quiet it was. All the onlookers were silent and any traffic had come to a halt. "I was not speaking loudly to him because I did not want others to hear what we were saying. We were speaking at a low volume."

But after about eight minutes of conversation, he was suddenly distracted and moved away. "More and more people were using their phones to film and he got pretty annoyed with that. He left me and went to send them on their way. He said to them their kids will pay. I was really hoping that no one would upset him, because that was all we needed."

Loyau-Kennett used the moment to approach the other man. He was standing a few feet away, motionless, near the car, holding a long knife in his blood-stained left hand.

"This is the photo you see of me and him in the newspapers," she says. "I said to him, 'You don't seem very involved in all this.' He said nothing. So I asked him if he wanted to give me what was in his hand. I didn't want to say the word. He didn't respond, but I could see in his face he was saying 'no'. He looked a bit overwhelmed. He didn't dare to move and was just holding this thing. So I asked him if he would like to go and walk away, or sit down. He said: 'No, no, no, no.' So I walked backwards and carried on my conversation with the other guy."

A woman then approached Loyau-Kennett tentatively and asked her to leave. "I was worried that leaving might have tipped him over the edge," she says. "So I said I would rather stay here talking and keeping him busy. The lady then asked me if I knew his intentions. I said he wanted to fight and kill the police when they come."

But then Loyau-Kennett noticed her bus starting to pull away. "I was suddenly thinking that my luggage is on board and I'm going to miss my coach to Cornwall. I thought to myself that I'd done as much as I could here. I looked at the guys and asked them if they were sure they didn't need a car or something. They said: 'No.' I said: 'Are you OK, because I have to go now?' They said: 'No problem.'"

Within 10 seconds of stepping back on to the bus, she says, a man rushed in shouting: "Lie down! Lie down!" Loyau-Kennett refused and watched out of the window as a police car arrived and shot both men in the legs, felling them and bringing the fraught saga to a close.

"I had no emotions at that point," she recalls. "But the people on the bus were screaming, so I had to tell them to calm down and that it was all finished now. I didn't want people stampeding down the stairs of the bus with all these babies and children around."

She texted her own children to say her bus had been delayed "because of a shooting". Her shocked son later rang to say her photo was on the internet and could he post a message online saying it was his mum. Within minutes he was inundated with media requests to speak to his mother. By the evening she had abandoned her coach journey to Cornwall and was put up in a London hotel in preparation for a breakfast TV interview the next morning.

She was utterly bemused by the reaction, she says: "The journalists kept saying: 'Do you realise you have stopped terrorists?' But at that stage I wasn't thinking of terrorists, or British soldiers, or anything like that. I just thought it was a street murder. He didn't look like a fanatic. He didn't have a long beard, or anything like that. They looked like regular guys."

A few days on, she has returned to her modest, three-bedroom house in Helston, a small town on the Lizard peninsula dominated by the nearby airbase RNAS Culdrose. Her home for the past five years since returning from a seven-year spell with her children in New Zealand, Helston is as ethnically monochrome as Woolwich is diverse. She admits the contrast is striking to her. (She is saddened by the "racism" she says she has witnessed in both New Zealand and Cornwall.) She is hoping to move to London soon, to be near her children and better opportunities to find work as a translator. "I love Woolwich. I love all the languages. I love going to the shops. They respect me and I respect them." Since returning to Helston, she says only a handful of local children have taken the time to congratulate her or say they saw her on the TV.

Loyau-Kennett, who now lives alone, apologises for not having had the chance to tidy up. "It's very cramped in here. I have too much stuff. That's the problem when you move from a big house to a small house."

Her sitting room is lined with floor-to-ceiling shelves full of books, CDs, DVDs and videos. They hint at her education and cultured, if eclectic, tastes. Books range from Balzac and Proust through to Michael Barrymore's biography and the complete set of Agatha Christie. French novels line the shelves in their hundreds. One shelf is devoted to French Bibles. Another boasts CDs by Chopin and Mozart, another Hitchcock thrillers and her children's old Disney cartoons. A portrait of Victor Hugo hangs on the door. But pride of place goes to the Mother's Day cards and Christmas cards from her children, Pawony, 24, and Basil, 23. (Basil described his mother as a "motherfucking badass" on Twitter.)

Her hallway is a shrine to her extensive international travels. A dozen clocks tell the time in different time zones, with a postcard under each clock – Times Square, New Caledonia, Cornwall, Tehran. Her former husband and her children's father is Iranian.

"When my kids grew up without their father," she says, "I made sure they knew about their Iranian part so that it was not missing in their lives and that later they could choose whatever they were most attracted to. They like Iran, without knowing really why. They are happy. You should always live within your cultural heritage. The other way never works. Even if you live in another country, you should always find time to gather together, speak the same language and eat your food together."

Both the hallway and sitting room are strikingly bedecked in union flag bunting and pictures of the Queen. A large union flag is pinned to her ground-floor window, facing out on to the street. "I'm a royalist," she explains enthusiastically. "I believe in kings rather than presidents. I organised a street party for the jubilee last year."

Loyau-Kennett is keen to stress that, despite her accent and being raised in France to English parents, she is very proud to be British. Her patriotism snugly fits the narrative of national hero bestowed on her by others, but it is clearly heartfelt. And it influences how she views the two men she confronted.

"I don't think these men have rejected Britain," she says. "I don't think they ever accepted it, even though they were born and raised here. Maybe converting to Islam was the only way they could find to be different, a bit like teenagers rebelling against their parents? They are bitter with Britain because of their life growing up. I think they are using Islam as an excuse. This third generation from immigrant families has had enough, it seems, and are now going back to their own roots, both in Britain and in France. We should do more to identify here the teenagers who are already showing signs of being unhappy about being in Britain."

Loyau-Kennett says she is "naturally rightwing". She adds: "I don't agree with the socialist thing where they praise everything rather than praising hard work. I'm proud that we are now represented by David Cameron rather than Gordon Brown. I voted for him."

The killers should now face "severe punishment", she says. "I will not waste any of my energy in hating, or even thinking further about these men. Yes, they deserve to be in jail because they killed a man who did a lot for society and who could have done a lot more in his life, and been an excellent father. The trouble with jail is that we have to pay for their keep. Will they stay in jail for ever? I don't think so, because of the judicial system these days."

Before her bus had arrived, one of the men had talked into an onlooker's cameraphone, quoting "an eye for an eye" in an attempt to justify his actions. Loyau-Kennett believes the killers should face the same retribution.

"If it were possible, then, yes, they should die a painful death," she says. "But we can't do that, unfortunately. They wanted to behead someone, so they should face the same. If they want to do something like this, they should have gone to where the action is [in Afghanistan, etc]. That is cowardice. They were egotistical. They are like the men who drive round thinking they are king of the road. It's just me, me, me. It's that thing where young men are bored. They should be jailed for murder, just as I think people who drive when drunk and kill someone should be jailed for ever for murder. No television in jail. Nothing. They must pay for what they did. But will that happen in this era of so-called human rights?"

Loyau-Kennett is deeply concerned, she says, about the direction modern society is headed. "I prefer the values of the past than the non-values of today, where most people don't seem to give a damn about others." The events of last Wednesday have magnified her feelings. She has particular disdain for some of the people who stood by recording on their phones, refusing to offer help.

"It annoyed me to see those people with mobile phones filming," she says. "They were doing it for money, with the idea of selling the footage. I was annoyed at what must be in their heads that they just wanted to watch and record the unhappiness of others. And then there was the stupidity of the mothers who had stopped there with their kids. The man could have reached them in five seconds if he'd run at them. It would never cross my mind to show a heavily bleeding body to my kids."

If people were scared, she ponders, why didn't they just run away? That's an understandable reaction, she says. "It's a horrible mentality that some people have these days. I think we have this culture now – maybe started by things like soap operas – where we have this unhealthy curiosity about other people's lives. You shouldn't just be there watching like it's on TV. By only watching they are actually interfering. Do something useful. Don't just stand there. Move away."

Loyau-Kennett sighs at the suggestion that she did something exceptional, selfless and brave: "I just instinctively did it. The same as if anyone had been crying and lying hurt on the ground. I am a mother. It was the same for the Caribbean lady. We both felt it was the right thing to do."