There are some actors' names – Errol Flynn, Marlon Brando, Johnny Depp – which, even if they were not famous, would still evoke images of romance, danger, drama. Then there is Bryan Cranston. It's hard to conceive of a more prosaic appellation. It's almost perfectly anonymous. Authentic but dully inconspicuous, it's a background kind of name. A solid name for a solid character actor.

Which is what Cranston was for almost three decades. On film and on television, he was repeatedly to be found in supporting roles, slowly building a reputation as a reliable and flexible performer who was equally adept in comedy and drama. Always in employment, he would crop up in shows such as Baywatch, Murder, She Wrote, LA Law and in minor parts in forgotten films such as Amazon Women on the Moon and The Companion.

His discreet profile was raised in the mid-90s by a recurring stint on Seinfeld, in which he played "dentist to the stars" Dr Tim Whatley. That led to improved supporting roles in better films and to the part as the bungling father in the popular family sitcom Malcolm in the Middle. Despite the upturn in his career, attention and awards remained centred on his fellow actors in the show. While his face – a curious mixture of a weak mouth and resilient eyes – became much better known, even fans of the show would have struggled to put a name to it.

What turned Bryan Cranston into a name that people began to remember, that producers sought to sign and that other actors spoke of with hard-earned respect was the part of Walter White, the mild-mannered chemistry teacher who turns to manufacturing crystal meth in the cable TV hit Breaking Bad. It was that rare gig in acting: a character lead, a part that not only called for detail and depth but which also propelled the action. The first series was screened in America in 2008 and Cranston won the Emmy award for outstanding lead actor in a drama series. He repeated the feat the following year and the year after that. Finally, after 30 years in the business, Cranston was an overnight star.

I met him earlier this month in London, where he was promoting Argo, a film directed by Ben Affleck that's based on the real-life story of six American embassy workers who were rescued from Iran during the 1979-81 hostage crisis. It's a slick and entertaining thriller in which Cranston plays the part of Jack O'Donnell, a wily CIA agent who oversees the "exfiltration".

It's not the main part – that's taken by Affleck – but it is the kind of role, like his equally deft performance in last year's Drive, that wouldn't have come Cranston's way a few years ago. He knows exactly why the quality of job offers has improved in recent years. "Breaking Bad has certainly raised the bar," he says. "There's been an effect on my career, there's no question about that. I can't just accept anything that comes along. It has to be at a level that's different but matches the level of writing of Breaking Bad. It takes a tremendous amount of work because you read massive amounts of product in order to find the nugget of gold. And the nugget of gold in this case is Argo, which is extremely well written."

He praises Affleck's skill as a film-maker and his ability to maintain focus as an actor while dealing with all the other responsibilities a director has to field. Perhaps sensitive to the criticism from some quarters that the film is an exercise in pro-American propaganda, Cranston is quick to make an unsolicited statement clarifying his and the film's liberal sentiments. "What I appreciate about the movie is that the film-makers decided to come clean by announcing the culpability of America in our foreign policy, that we helped to orchestrate the regime change in Iran putting the Shah in power. The bad guy in the movie is really an ideology. Any kind of civil rights oppression is wrong."

Mini-lecture over, he returns to the question of the Breaking Bad effect. "As it's a well-told story," he explains, "it attracts attention from storytellers themselves, because it's so intricate and dark and twisted."

It's also the story of a man whose brilliantly creative mind has been imprisoned in mediocrity, a man who has silently acquired a lifetime's pent-up frustrations. What liberates Walter White is a diagnosis of terminal cancer. Knowing that he is soon to die, he begins to live, by using his chemical expertise to produce the purest and most potent methamphetamine the market has ever seen.

Given the powerful conviction and credibility that Cranston brings to White's metamorphosis, it's tempting to see White's buried resentments as a metaphor for the disappointments of his own career. However it's not a temptation to which Cranston is given, at least not publicly.

"No," he insists, "I was very happy with my career. If you have a level of expectation in your life that you have to be a quote-unquote star, whatever that means, you might be setting yourself up for failure. But my expectations were that I would be a working actor, that I could honestly say that I make a living as an actor and that was achieved when I was 24. Above that, the world doesn't owe me anything, the business doesn't owe me anything. Anything that is gained is through hard work."

All of that may be true, but you only have to spend half an hour in Los Angeles to sense the atmosphere of envy and insecurity that hangs over the city like its smog. Everyone knows exactly how well everyone else is doing and no one is doing well enough. To maintain an attitude of professional contentment as a middle-ranking character actor would be an act of Zen-like forbearance, particular if you harboured ambitions, like the rest of LA's inhabitants, to be something more.

He gives a glimpse of the inner drive that must have taken him through all those walk-on parts in the 1980s and 1990s when he says: "In order to be an actor you really have to be one of those types of people who are risk-takers and have what is considered an actor's arrogance, which is not to say an arrogance in your personal life. But you have to be the type of person who wants the ball with seconds left in the game. The masses don't want the ball. They don't want to be responsible for not making the shot. Actors need to want that chance. Give me that chance."

And that chance, as he is keen to make clear, is often a matter of chance. "Luck is a component that a lot of people in the arts sometimes fail to recognise: that you can have talent, perseverance, patience, but without luck you will not have a successful career."

Cranston's luck was to be cast as an antisemitic lunatic, terrorised by sound waves, in an episode of the paranormal drama series The X-Files. The episode began with Cranston's character driving wildly into the desert. Broadcast in 1998, it was written by Vince Gilligan. Almost 10 years later, Gilligan recalled Cranston and asked him to take the lead in a drama he had conceived about a middle-aged man whose end-life crisis thrusts him into the darklands of America's illicit drug trade. The opening scene saw Cranston once more driving wildly into the desert.

Since that moment, the drama has steadily and sometimes abruptly developed across five series – the fifth and final season is now showing in the States – into an intimate and fascinating study of character, motivation and moral choice. The first two series were broadcast on the FX channel in Britain but since then viewers have either downloaded the show – legally and illegally – or caught up with it through renting or buying series DVD sets.

However it has been viewed, the series now demands to be spoken of in the same breathless breath as those other mammoth American dramas The Sopranos and The Wire. Although Breaking Bad can't rival the narrative breadth and complexity of those two television landmarks, and it has also taken more artistic licence with its plots, it does match them in terms of originality, intelligence, sense of place and dramatic engagement and certainly outdoes both in cinematography.

When filming began, Cranston had little idea of the particulars of his character's travails, only a general sense of his moral trajectory. "I knew Vince wanted to go from Mr Chips to Scarface," he says. "I knew he wanted to go from a good person to a bad person. So it was up to me to figure out, through his writing, how to make it feel plausible and justifiable. Some people are saying recently, about some of the things he's done: that's not Walt. I say: it is now. He's a very pragmatic man, very scholarly, very exact. Chemistry is an exact science. No guesswork. But now because his emotions are gone, he's doing things that are a little erratic. He's impulsive at times."

If some viewers have expressed doubts about Walt's evolution or, perhaps more accurately, devolution, plenty of others see it as an epic voyage into the American underbelly. No less an authority on storytelling than Stephen King even suggested that Breaking Bad had "surpassed The Sopranos". Describing the series as an "American classic", King said that Cranston and his co-star Aaron Paul had "turned in the best performances I've seen in years".

What's beyond doubt is that the relationship between Walter White and his former pupil and troublesome sidekick, Jesse Pinkman (Paul) is one of the great unlikely double acts of television or film, an odd couple to beat The Odd Couple. Squeezed into their prickly partnership are themes of youth and age, rectitude and dysfunction, love and hate, loyalty and mistrust. And the whole dynamic is balanced on a knife edge, forever teetering between black comedy and even blacker tragedy.

Cranston speaks of Paul with obvious paternal-like affection. "I love his parents – I know them pretty well – but he could be my son almost. I'm old enough to have fathered him and I do have fatherly feelings towards him. Occasionally I give him advice and just try to guide him to where he needs to be, at least from my point of view."

In The Odd Couple it was Jack Lemmon who played the role of the fastidious flatmate. And it was to Lemmon that Jane Kaczmarek (Cranston's co-star in Malcolm in the Middle) has compared her one-time screen husband. "He's like Jack Lemmon," she said three years ago, "except now he's doing Days of Wine and Roses or The Apartment."

Lemmon, it turns out, is one of Cranston's acting heroes. "I appreciated his intensity, his zest for it. He would say: it's magic time. I have the same attitude – it's a fun adventure for me. And for Jack to go from comedy to drama so fluidly – I wish I'd had the opportunity to meet him.

"Dick Van Dyke influenced me a lot – you know, his physical comedy and his ability to be loose in his body. Rod Steiger was another actor I thought was immensely talented. Mark Rylance is someone I have a huge man-crush on. If I could watch him just drink tea I'd sit there for an hour."

In person, there's little that's coy or comic about Cranston. He comes across as amiable but almost coolly professional and much more physically confident than he tends to appear on screen. If you look closely at his performances, there are flashes of Van Dyke in his chaotic father in Malcolm in the Middle, but there is something consistently Lemmon-like about his overall work as actor. It's a sort of contorted or neurotic decency that can play for laughs or tears, a perplexed, put-upon pathos that you root for in spite of everything. And in Breaking Bad there is an awful lot of everything.

Taken together, it amounts to a serious challenge to the viewer's sympathies, let alone those of commissioning executives. Although American cable TV has proved itself to be remarkably open to difficult subject matter, the idea of a middle-aged, middle-class, middle-American peddling crystal meth is not what you'd call an easy sell. All the major cable networks turned it down, and although the series was developed at FX, it too passed.

AMC, its eventual home, embraced the concept but had reservations about Cranston. Nonetheless Gilligan knew that he was vital to the show. "Because he's so decent and likable," Gilligan has said, "Bryan allows you to comprehend why he does what he does, even if you don't agree with it."

Along with its setting beneath the magnificent wide-open skies of Albuquerque in New Mexico, one of the most distinctive aspects of Breaking Bad is the crystal meth scene. In common with Cranston, it's resolutely unglamorous. There are no sexy fringe benefits, no alluring distractions. It's either the cold science and ruthless business of the producers or the violent highs and grimy dissipation of the consumers. Although the war on drugs is depicted with all the futile death and destruction that wars wreak, it would be difficult to describe the show's message as explicitly, or even implicitly, anti-prohibitionist.

Cranston isn't interested in getting into the politics of the situation. For him, the role of crystal meth in the series was fundamentally dramatic. "If it was marijuana we were dealing with, no one really cares," he says. "But the fact that it's this very heavy scourge-of-society type drug means there is far more at stake. It also makes it much more difficult for Walter to be able to compromise his ethics."

When pressed on his views on drugs, he takes a classically liberal libertarian stance. "I think marijuana should be legalised," he says. "There should still be restrictions on being intoxicated, and there should be age limits and so on, but I think it should be legalised. I also think prostitution should be legalised. What two adults do in private shouldn't be any of my business, and in a pragmatic way you'd save millions upon millions of dollars not incarcerating these young women."

Cranston has been married for 23 years to the actress Robin Dearden. They met on a TV show called Airwolf. He played a kidnapper and she was his hostage. "We still love each other. She's with me now and we like to travel together," he says a little defensively about Dearden when I ask about his five-year screen relationship with Anna Gunn, who plays Walt's wife, Skyler, in Breaking Bad. He and Dearden have a teenage daughter and he divides his time between Los Angeles and Albuquerque, where for the past five years he has spent six months out of every 12 filming.

He grew up in the San Fernando Valley, the vast suburb that lies beyond the Hollywood Hills. His parents were both actors. "They met in Hollywood in an acting class in 1948, after the war when everything was new and fresh and alive and full of potential and possibility. It must have been a very romantic time. And they had their romance."

His mother stopped acting to raise a family – "I think she resented the fact that she gave up that part of her life" – and his father was often out of work. Perhaps aware of Hollywood's vicissitudes, Cranston decided to join the police. He joined a police explorer group when he was 16 and graduated first out of 111 cadets. "I think I would have been a good policeman. They have to have a curious mind and a sceptical view, to not just believe everything they see but uncover every single element and be detail-orientated, to know protocol and keep a cool head under fire. And I think that's something I could have done."

The reason he didn't, he says, is because he discovered girls.

"I was also taking an elective theatre class at college and the girls in theatre class were far prettier than the ones in police science class. In my job as a young actor I was supposed to kiss this girl. That was my job. I've been trying to do this all my life and now you're telling me I'm supposed to do this? I love this. It's like you stepped into a fantasy. So at 19 years old this was the basis of my decision-making. No more police work, I'm going to be an actor."

Almost 40 years later, few would argue that he made the wrong decision. He may well have made a fine detective but in Walter White, the chemistry teacher with lung cancer, he has created one of the most memorable villains ever to don a black hat.

• This article was amended on 29 October 2012. The original misspelled Robin Dearden's name as Robin Deardon throughout. This has been corrected.