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It goes like this: The ragged but reflective young orphan, born into an urban hell of stench and adventure and violence, loses his one source of protection and falls into the hands of a child-crime-gang master, who happens to be a dreadful ethnic stereotype.

The boy gathers the wit and cleverness to escape and joins a much-tougher young companion on a whirlwind tour that reveals hard truths: He falls back into crime, catches a woman's eye, struggles to stay ahead of the law, witnesses a terrible act of violence and, finally, is freed into unimaginable wealth through a profoundly unlikely stroke of chance.

In 1838, when Charles Dickens told the story, it marked the birth of an exciting new form of social-commentary drama – let's call it the ghetto picaresque. Now, 170 years later, his countryman Danny Boyle may become a winner at next week's Academy Awards for telling exactly the same tale in almost exactly the same way, but shifting the location slightly.

Bethnal Green, meet the Dharavi slum; Oliver Twist, meet Slumdog Millionaire.

What has made this genre so enduringly successful is not the melodramatic account of a young person's rise from squalor and poverty to something more elevated. That story had been doing great box office for centuries – including such hits as Cinderella, Moses, Moll Flanders and Jesus Christ.

What Dickens introduced was a new character – the slum itself. The East London shantytowns of Clerkenwell and Bethnal Green loom so large in Oliver Twist that they serve as the novel's main antagonist, throwing all manner of spectres and challenges at the hapless Oliver. At the end, while Oliver is fixed and catalogued, the slum remains a blank-faced mystery.

Danny Boyle's Mumbai, which at the story's outset has not yet been robbed of its name Bombay, is similarly compelling, similarly menacing, similarly inscrutable. It appears as a vast and gorgeous figure, responsible for most of the film's plot twists.

I've spent plenty of time in the Azadnagar and Dharavi slums, which the director has used interchangeably as the film's setting, and he captures them very well, with their combined population of more than a million, their near-total lack of sanitation, their extraordinary range of industry and creative activity, their witty and engaged populations, their many rootless children and their unimaginable density of 18,000 people per acre.

At the end of the movie, just like at the end of Oliver Twist, you're left wondering not what happens to our boys – we've had enough of them – but what happens to the slum.

We know something must happen to the slum, transforming it just as the boys are transformed by their experience. Both stories play a game with us that is characteristic of the genre: They treat the slum as a sort of urban flypaper that seems to catch all those who have failed in life. They're able to pull off this trick by erasing the parentage of the protagonists, so the boys seem to have been dumped here.

Neither story addresses the crucial question, “Why are their families living here in the first place?” The answer is that they're finding a better life.

In nations in transition, from industrializing England to present-day India, slums are created when people abandon the deadly and inhibiting practice of peasant agriculture to find something better for their children, and usually finding it.

We are aware of this on the periphery of Slumdog Millionaire – we see the bulldozers at work, the high-rises going up and new slum accretions forming along the building sites. People want to be there.

We may not know, but we are somehow aware, that the main obsession of Mumbai slum dwellers, according to studies, is not to escape their hell but rather to stay – to get ownership of the tiny patch of land beneath their corrugated-metal hut and see their property values increase, as many have done. Mumbai's slums, for all their stench and chaos, are seen by their dwellers, in the words of researcher Vinit Mukhija, as “a valuable real-estate asset” that can be used as equity in business formation. These people aren't losers – they're speculators.

We realize this in reading Oliver Twist, because we know that Clerkenwell is now a nice neighbourhood and Bethnal Green is not a destitute slum any more. It certainly was in the 19th century: East London was, by every account, exactly as haphazardly built, densely populated, crime-ridden, unsanitary and packed with lost children as the Mumbai slums are today. Its social and economic conditions were in some ways even worse.

Yet for most of the past century, East London has been, as sociologist Kate Gavron told me, “a very consistent success story in creating integration and success for each new immigrant community that comes along.” It's transformed successive waves of Huguenot weavers, then English and Irish farmers, then East European Jews and then Indians and Bangladeshis into successful and prosperous urban residents.

Dickens's East London changed very slowly: Bethnal Green had been a pretty destitute place for a century by the time Oliver Twist found himself holed up with Bill Sikes there: People born there tended to stay poor. It really was flypaper.

Studies show that it began to turn around in the final quarter of the 19th century and really took off on the edge of the First World War. Suddenly, it was a place of very quick upward social mobility: Your chances of escaping the poverty of your birth rose from 1 in 3 at the beginning of the 19th century to 1 in 2 at the end – at which point a third of middle-class Londoners had been born in the working class.

Three things changed: Public education, social assistance and the ability for anyone to borrow money and buy their own housing.

It took more than a century for a young London to discover this formula and to make its stealthy escape from the evil gang masters' clutches. Mumbai actually has a head start: Its people already know that education, assistance and ownership are what slum dwellers need.

It still has a long struggle against terrible poverty to face, but in many ways its situation is less dire than the one faced 170 years ago by its older urban sibling. So little brother Mumbai has just as good a chance of breaking free, finding love and ending on a lively dance number.