Class is a dangerous subject, taboo in mainstream politics. The riots brought out a rash of comment implying that there is one great, respectable middle class and an inexplicable underclass beneath, quite unconnected to what's been happening to wages, incomes and the stretching of social bonds.

Britain is adopting the American political dishonesty of disguising ever-widening income differences by calling nearly everyone "middle class". More than 70% now call themselves "middle" – because that's the way politics has led and because, post trade unionism, people no longer know where they stand on the earnings scale.

The convenient political myth says class is dead. Downton Abbey deference is no more, and look how differences among the young meld into universal estuary and mockney. Classlessness may be modern and hip – yet birth determines destiny more certainly than 50 years ago. Never mind Hyacinth Bucket niceties of napkins over serviettes, class matters more not less than it did, and it needs saying loudly.

I have been making a BBC radio series, The Class Ceiling, which starts this week. Before setting out I asked everyone I came across if they had a story about class: everyone has – either working class people confounded by middle class snobbery, or privileged children embarrassed by being posh. Pretence, shame, pain, guilt, anger – the stories tumble out. Scratch below the surface denial and class is everywhere, as I found in making these programmes.

Nobody in the BritainThinks poll admitted to being "upper", so you have to gauge what people mean from who's talking. Those calling themselves "middle" stretch from euphemisms for the highly privileged – the 7% with children in private schools – all the way to families struggling on the edge to pay a half-mortgage on an ex-council house. Only 24% call themselves working class now. Where once the label was a badge of pride (67% claimed it in 1988) now those self-defining as working class say despondently that it only means "poor" and "low-paid" these days.

Of course people sense how far birth still determines fate: those who make it from humble beginnings are admired because rags to riches stories are so rare. The great majority of those in professions and good jobs were born to them. My father was a writer and journalist: would I be writing this if I hadn't had a head start? The successful are smug if they deny their luck, either in birth or other good fortune, including talents. Too often "effort" is overclaimed and luck ignored by those eagerly justifying their class and income advantage over the very hard-working low-paid.

Making these programmes has reminded me how far the language of class has been expunged from politics. The triumph of grocer's daughter Margaret Thatcher put paid to her party's toffs who sneered at her cohort as "garagistes". John Major followed on with his promise of the "classless society". The party so effectively buried its class history on Alec Douglas Home's grouse moor that it now claims as an accidental irrelevance that its front bench happens to harbour so many multimillionaires and old boys of top public schools, from whence come 58% of Tory MPs (15% on Labour benches).

Labour shies away from crude class attack, probably wisely saying it's not where you come from but what you stand for that matters – though they might point out the frequent synergy between them. New Labour was so afraid of being cast as a cloth cap, northern party of dying industries that Tony Blair proclaimed "the class war is over". He chose to end the war, not class. He could have galvanised the great majority that have been cheated by an overweening super-class but thought it electorally necessary to mimic the Tory myth of the undifferentiated big-tent "middle".

My series touches little on the party politics of class, exploring instead the social realities beneath. Why do people falsely believe class is fading? Because the postwar years did see an exceptional upward surge, as a great increase in white collar and middle managerial jobs changed a two-thirds working class society into two-thirds middle class: it's worth noting it happened not via education but the changing labour market. Then social progress stopped – a study comparing the fate of children born in 1958 with those born in 1970 shows the latter more hermetically sealed into the social class of their birth.

British children's achievement is more closely linked to parental status than in most developed countries. Only 21% of children from families in the lowest fifth of incomes get five good GCSEs, against 75% from the richest fifth. Class trajectory is almost set before they get to school. Usha Goswami, a Cambridge University neuroscientist, explains how much the first year of life shapes the brain, babies thriving according to the love, language, empathy and intellectual stimulation they receive. All parties now talk about the importance of early years, yet we invest least in the youngest.

And all parties avoid one inconvenient fact raised by Oxford's John Goldthorpe: social mobility goes both ways. If poorer children rise up, some from higher classes must fall. Room at the top is limited, and there is little prospect of another 60s-style surge in good jobs. Politicians pretend "it's not a zero sum game", but ask recent graduates discovering good jobs don't multiply to greet more well-qualified applicants.

Class is a tangled web of education, taste, history and illusion – but follow the money, and income matches class pretty accurately. GDP has doubled since 1978, but only the top 10% have seen incomes grow at or above that rate, twice as fast as the median and four times faster than the bottom 10%. As universities minister David Willetts has honestly acknowledged, "Western societies with less mobility are the ones with less equality too." When the income gap is wide, few cross the class divide, so remedies may lie less in schools than in the society they reflect.

As Richard Wilkinson, co-author of The Spirit Level, says, "Boosting social mobility without addressing income inequality is like trying to diet without worrying about calories." Avoiding the word class, all parties instead urge social mobility. But they never say why we should bother swapping round which people are mega-rich and which are dirt poor, when it's the unjust gulf in wages and rewards that does the social damage.

• Polly Toynbee has replied to comments in the thread here

• The Class Ceiling begins on Radio 4 on 1 September at 9am