Clive Stafford Smith's son Wilf is only three, but must have formed a pretty low opinion of the police already, because when he found out that a friend's father was an officer, his mother had to explain that there are some good policemen. This revelation clearly made quite an impression on the toddler. He promptly sent his parents to prison.

"He comes into the living room the very next day," his father giggles, "and says: 'Daddy, into the kitchen', and shuts the door behind me. So I'm saying: 'Wilf, we're going a little far here, now let's talk about the presumption of innocence, the need for evidence. I mean, what am I even supposed to have done?'" Not for the first time in Stafford Smith's life, his appeal to due process fell on deaf ears. The headteacher at his son's nursery took him aside later that week and told him: "Do you know, this morning Wilf sent the entire class to prison!" Stafford Smith hoots with laughter. "So he's going to become either a hedge fund manager or a prosecutor."

Stafford Smith has always been one of my heroes, but I'd always been slightly apprehensive about meeting the lawyer. What if he turned out to be dreadfully earnest – a sort of humourless Peter Tatchell of death row? To rightwingers who deploy the term "do-gooder" as an insult, his CV reads like their worst nightmare; head boy at an Oxfordshire public school, he turned down a place at Cambridge to study journalism in the US, with a hazy but heartfelt plan to "put an end to America's tryst with the death penalty". Staying on to study law, he came home in the holidays to work for his cousin's ready-mix concrete company, because "I wanted to be reminded that if these men carried their lunch boxes to work every winter's morning for less than £1 an hour, then I should accept the same pay to do labour that I loved."

It's the kind of sentiment that has Daily Telegraph readers reaching for the sickbag, but it's precisely what he went on to do, toiling for a pittance to save convicts from execution for 20 years, before coming home in 2004 to run the charity Reprieve, representing prisoners on death row all over the world. Personally, I would give anything for a CV like his, but do see its scope for tiresome sanctimony.

But Stafford Smith turns out to be positively bouncy with good humour and silly jokes and an eye for the absurd – so much so, in fact, that at 53 he retains an almost teenage quality. At public talks someone always asks if there is anyone he wouldn't represent, to which he replies: "Well, I'm sorry, I just couldn't represent a Tory." The only time he regretted it was when "I'd forgotten – oh fuck, my mother's in the room – and she's voted Tory since 1642." He can cope with serial killers – "It's just serial people who vote Conservative all the time I find very difficult to understand" – and he and his wife Emily, a fellow lawyer, were married in jail by one of his clients after they had got his death sentence commuted to life. "It was so sweet, it was gorgeous. I loved it, I'm so proud of it." Was the murderer authorised to officiate? "No! He's not authorised, but who cares?"

Stafford Smith's new book, Injustice: Life and Death in the Courtrooms of America, isn't exactly a barrel of laughs. But it reads like a thriller, gripping and appalling by turn, following the case of a client convicted of a double murder and sentenced to death in 1986. In itself it's an extraordinary story, exposing incompetence and corruption, dodgy coppers and Colombian drug cartels, and to this day its protagonist remains behind bars – which is why Stafford Smith wrote the book. "I feel so guilty for failing him, and I thought I've got to take his case to the court of public opinion." But in doing so he tells a greater and more troubling tale still, about the Kafkaesque madness of a justice system that appears engineered to deliver anything but justice.

"You start thinking, how could I have failed Kris [Maharaj, his client] so palpably, for so long? I started thinking about things, and I feel an idiot, but I'd just never really stopped to think about how the system is structured in a way that's so flawed. It gets you at every turn. I've often said, in a sort of glib way: 'I hate representing innocent people.' But I'd never really stopped to think how it is that an innocent person is so certain that they didn't do it, that they can't fathom that 12 people could find them guilty."

Maharaj was a successful businessman when he was charged with the murder of two business associates. Not believing for a minute that he could be found guilty, he hired a spectacularly hopeless lawyer, in large part because he offered his services for an affordable fixed rate. Why, Maharaj reasoned, spend a fortune when it's obvious I'm innocent? But a lawyer on a fixed rate has a financial disincentive to spend more than the bare minimum of time on a case. Once convicted, the defendant can hire a new and better lawyer to represent his appeals – but due to a bizarre law known as a "procedural bar", that new lawyer can't submit any new evidence that the rubbish one should have brought up the first time around, because the defence case is deemed to have "waived the right" to mention it by omitting it the first time around.

Opposing him are police and prosecutors whose professional careers – and, Stafford Smith would argue, moral sanity – depends upon an implacable belief that no defendant could conceivably be innocent. There is a common view that the justice system is skewed in favour of the defendant, but nothing, he says, could be further from the truth.

"What made me think about this was a conversation with two cops, who were lovely, and who had 54 years of service between them. And I was curious, so I asked them: 'How many times in 54 years do you think that maybe, maybe, you arrested the wrong guy?' And they said: 'Oh, never.'"

Not one of the judges on the US supreme court of justice has ever worked as a defence counsel, and district attorneys are elected – so they have a vested interest in appearing draconian. Stafford Smith cites a study that found that more than half of US prosecutors do not believe in the presumption of innocence at all. "Fascinating, isn't it? But the thing you have to ask yourself on a human level is, could you, as a person, drive to work every day saying: 'I wonder if I'm going to put an innocent person in prison today or not'? You just can't do that as a human. So naturally, the people who do this job believe that everyone is guilty. And it's something the system doesn't take account of. But it's sort of obvious, isn't it?" As a consequence, the system legislates for malpractice, if not outright corruption, by police and prosecutors who believe they are merely doing whatever it takes to deliver justice.

Even the concept of "reasonable doubt" is no safeguard against miscarriages, Stafford Smith points out, because nobody knows what it means. As a lawyer he's prohibited from even asking jurors what they think it means, or discussing the question in court – so the entire judicial process rests upon a concept shrouded in mystery. "We cannot loudly proclaim that the burden of proof is central to the system," he writes, "yet then assert that we cannot begin to define it."

What does he think it means? "I think it means: can you imagine that this could have happened some other way than the prosecution says?" But if the prosecution tells a jury there's only a one-in-a-million chance the explanation offered by the defence could be true, jurors assume the defence must be lying. "Because if the probability of something happening is one in a million, you think: 'Well, it's never going to happen to me.' But the probability of it happening to you in Britain, say, where 60 million people live, is that of course it's going to happen. A one in a million chance can come up all the time. But the thing is that no one will believe it."

Maharaj's death sentence was eventually overturned by Stafford Smith. But surely the risk of execution was not the only feature that made his a uniquely American story? Stafford Smith concedes there is "probably" less corruption in the British justice system, and that defendants are better funded. "But pretty much all of Kris's story could happen here. There's no less bias here." In some ways, in fact, it is worse.

"The jury system in this country is utter insanity, because you're not allowed to talk to jurors before or after the trial. There's no way of knowing if they did their job properly. And the idea that the defence has to rely on the police for the investigation? Total insanity. I've never met a defence lawyer here who has done any factual investigation for themselves. Total insanity. And the whole notion of a barrister – that he shouldn't have an emotional relationship with his client? Insanity. You cannot represent someone, and meaningfully put them across to the jury, if you don't have a relationship with them."

Britain's adoption of American-style victim impact statements has only made matters worse, he argues. "The victims' families have been told their catharsis is going to come from punishment. And it's just cruel, because it doesn't. They just get exploited. I think that's probably the area in which we've been most unkind to victims."

Our system is less disastrous than the US's in just one crucial respect: "Our results are not as catastrophic, because we don't kill people."

Stafford Smith thinks the US will unquestionably abolish the death penalty: "In my lifetime, hopefully, depending upon how many gin and tonics I drink." He has witnessed six executions, all of clients he failed to save, and is haunted most by the electric chair. Having witnessed an execution by lethal injection myself, and written about it, I wonder if he worries about the unpleasantly pornographic problem of evoking the full horror. "No, I'm glad to have had the experience. Not because it isn't horrid, but when you're talking to a jury, if you've had that experience it gives you so much more power to talk about what it is like."

The bigger problem for Stafford Smith becomes clear as the interview goes on. What he really wants to talk about is something he worries will alienate people. "It's not something I really want to get into right now, because I need to preserve just a tiny bit of credibility. I will write a book about it one day – when I'm close to death, so it doesn't matter any more – about why the whole underlying concept of the justice system is just ridiculous. Total madness. But I don't want to lose people's attention and make them stop listening because they respond in an emotive way. I don't want to alienate the whole world. "

But he can't help talking about it anyway. His anxiety probably comes from spending 25 years in the US, where it probably would sound like heresy, but to me it sounds perfectly sensible.

"Let me ask you," he says, "about the most despicable thing you've ever done in your life, that you're most ashamed of, that you don't want anyone to know. My guess is we'd agree that it's not a criminal offence. It's just something really nasty that you did to someone you love. Now, let's compare the harm in that to the worst criminal offence that's ever been done to you. Which is what?" I have a think, and all I can come up with is having been burgled. "So, how much impact did that have on you?" It was really inconvenient – but emotional impact? None.

"Zero, right. And yet if I'm right, the thing you did, that you're actually ashamed of, inflicted a lot of harm on the person you did it to. Yet the thing we define as a 'crime' – for which some young black British person would get maybe four years in prison – has no impact on you at all. Why is it that we define our criminal law in terms of utter irrationality, where nasty things that you and I do have no consequences legally – and things that are really quite inconsequential, poor people end up in prison for. Why is that?"

I didn't much mind being burgled, I agree, but lots of people do enormously. "But that's because we've trained people to have these idiotic attitudes! It's crazy." And when it comes to genuinely devastating and heinous crimes, he goes on, our response is if anything even crazier. "Because the worse the crime, the more obvious the explanation. There's a reason why it happened."

Put simply, when someone does something bloodcurdlingly awful they are pretty much by definition not bad but mad. He would include Tony Blair and George Bush in that category – "Oh yes, definitely, they were psychotic" – and can't fathom how anyone could regard a sadistic killer, for instance, as remotely sane. Stafford Smith's own father suffered from mental illness – he once memorably handed his seven-year-old son £200 and told him to leave home and look after himself – "And it was a huge relief to me to realise he wasn't a bad guy. He just was not on our planet. He didn't understand the difference between right and wrong." The same goes for most of his guilty clients, he believes. "But we just have this mad approach to madness."

I'm very much looking forward to the book he writes about this, though I hope we don't really have to wait until he's on his deathbed. In the meantime, to anyone who suspects Stafford Smith must be both bad and mad for holding such views, I offer this in mitigation.

"No please don't say anything about this," he begs, the moment it's out of his mouth. "I don't want to look like a prat or anything. It will make me look horribly sanctimonious." In the current climate, I tell him, I very much doubt it.

Stafford Smith draws no salary from Reprieve. Instead, he receives a grant from the Joseph Rowntree Foundation for being a "visionary" – for which he is not liable to pay income tax. But every year he works out how much tax he would pay, were it a salary, and sends it off to the Inland Revenue.

"I can't stop you writing that," he concedes, "because I believe in free speech." But he looks mortified. "I just don't want to look like a plonker."