The Etonian still strolls through the streets in his tails (although minus the top hat these days); the Harrovian still sports his straw hat. Not only have the grand old public schools survived the 20th century, they and a host of former grammar and direct-grant, prep and pre-prep schools make up an independent sector that is flourishing as never before - and producing results which few state schools can match.
At the turn of the last century, the private sector was dominated by 64 boys' public schools educating about 20,000 pupils and by a much smaller but fast-growing band of girls' public schools.
Today, there are 2,400 independent schools in the United Kingdom educating nearly 600,000 pupils, with roughly equal numbers of boys and girls. In England alone, they educate some 7 per cent of all school-age children, rising to nearly one in 10 secondary pupils and nearly one in five sixth-formers.
Fees range from pound;3,000 to pound;4,000 a year for a small day preparatory school to pound;15,500 a year for a major public boarding school.
The character of independent schools has also changed. In The Public School Phenomenon, Jonathan Gathorne-Hardy describes the boys' public schools of 1900 as "a fiercely disciplined and restrictive monolith, entirely obsessed with teaching games and, except for a select and brilliant few to whom they taught the classics, philistine to a degree, despising and ignoring, in particular, science; they were frenziedly repressive about sex, odiously class-conscious and shut off into tight, conventional, usually brutal little total communities".
As the next century turns, the typical independent school is, by contrast, a day school in a suburban area, just as likely to be for girls as for boys, or mixed - which was rare in 1900 - and quite possibly a former direct-grant school with a history of collaboration with the state.
Corporal punishment is only a memory. Games are still important but no longer all important. While the independent sector remains the last redoubt of the classics, maths is now their most popular A-level subject and science is more popular than in state schools. The arts are pursued with zeal, with some of the richer schools boasting art schools, music centres and theatres that would not disgrace a small university.
Boarding has fallen sharply since the 1970s, although the decline has levelled off. Today, only one in four pupils in the leading boys' and co-educational public schools is a boarder, compared to one in eight in the leading girls' schools and one in 10 at prep schools. Where boarding survives, it is much more child-friendly than formerly, with frequent visits home allowed and bedrooms more redolent of Laura Ashley than the workhouse.
Above all, independent schools offer an excellent standard and breadth of education. With their increasingly selective intake, combined with small classes, good facilities and highly qualified teachers, they take all but a few of the top 100 places in A-level league tables. Old names such as Winchester, Westminster, St Paul's and Eton appear regularly at or near the top of the list, along with girls' schools such as North London Collegiate and Wycombe Abbey.
Most of the changes have taken place since the 1960s, although the first half of the century did see well-meaning but doomed attempts by governments to bring the independent sector closer to the state system.
In 1919, Head Masters' Conference schools offered the first places to state-aided former elementary schoolboys. In 1926, the direct-grant list was established, giving schools the half-way house option of being self-governing but financially dependent on a direct grant from the government.
By 1942, the public schools, conscious they were not keeping pace with the social upheaval caused by two world wars, asked for an inquiry to "consider means whereby the association between the public schools and the general educational system of the country could be developed and extended".
The resulting Fleming Report, published in 1944, proposed two schemes: one to replace the direct-grant system with a needs-blind admission scheme based only on ability; the other designed for boarding schools, which would agree to give at least a quarter of their places to pupils from primary schools on means-tested bursaries.
But the report appeared after the Education Bill, that was to become the 1944 Act, had been published, so the impetus for radical action was lost. And R A Butler was able to say afterwards, with some satisfaction: "The first-class carriage had been shunted on to an immense siding."
Instead of radical reform, the direct-grant list was extended and some local education authorities used their powers to pay fees for pupils to attend independent schools.
Two decades later came the great move to comprehensive education: circular 1065 and all that. Harold Wilson's Labour government set up the Newsom inquiry into public schools in 1965, which proposed that a number of public schools would become "integrated", admitting assisted pupils from maintained schools to at least half their places and taking a more nearly comprehensive intake.
Once again, the Newsom report was criticised from all sides and never implemented.
A further inquiry under Professor David Donnison proposed ways in which independent day schools and direct-grant schools could take part in the move to comprehensive reorganisation. But the general election of 1970 and a change of government intervened before any action could be taken.
In fact, rather than integrating themselves into a comprehensive system, most independent schools moved in the opposite direction. As Andrew Adonis and Stephen Pollard write in A Class Act, "the egalitarian educational reforms of the 1960s, notably the replacement of grammar schools by comprehensives, precipitated ... the conversion of the public schools into fully fledged meritocratic academies".
When Labour returned to power and, in 1975, offered direct-grant schools the choice of joining the maintained sector as comprehensives or going completely private, more than two-thirds of the 170 schools chose the latter.
In 1979, Margaret Thatcher's Conservative government came in pledging to restore the opportunities lost by the withdrawal of the direct grant by introducing the Assisted Places Scheme. Covering many of the same schools, it was introduced in 1980 with places for 5,600 pupils and, at its peak, was subsidising some 34,000 children. It was, however, bedevilled by the suspicion that it had been hi-jacked by the middle classes - by "the genteel poor or by clean break divorcees", in the words of one headmaster.
Labour's hostility to independent schools had continued to grow, culminating in a motion to abolish them approved by seven million votes to 7,000 at the Labour party conference in 1981.
But this was watered down during the 1980s to a simple commitment to review the schools' charitable status, which gives them substantial tax advantages. By the time of the 1987 election, the only firm pledge that remained was to abolish the Assisted Places Scheme and use the estimated pound;100 million saving to reduce infant class sizes.
The new Labour Government, at the instigation of its public school-educated Prime Minister, quickly turned to building bridges between the state and independent sectors.
In 1997, Stephen Byers, then minister of state for education, became the first Labour minister to address an independent schools' conference. He announced government funding for partnership schemes between the two sectors. Today, there are more than 100 in operation, ranging from shared classics classes to joint projects on information technology.
Through all the upheavals of the past 30 years, and with only a small blip during the recession of the early 1990s, the independent sector has continued to grow. Even the ending of the Assisted Places Scheme did not lead to an overall drop in numbers, with the boom in very young pupils (40 per cent of prep schools now take children aged two) and in day girls more than compensating for a small drop in the secondary intake.
There is evidence of greater mobility between the independent and state sector. Parents in areas, such as Kent, where there are still many selective schools, may decide to spend money on prep schooling to increase their child's chance of a good, free, secondary education; or a pupil might spend the main secondary years in an independent school before opting for the greater freedom of a state sixth-form college.
But partnership schemes and mobility between the sectors cannot disguise the fact that the gap between the two remains huge. Peter Lampl, the millionaire philanthropist, never tires of repeating that the chances of getting to Oxbridge from an independent school are 30 times greater than from a comprehensive.
He is funding a needs-blind admission scheme at Liverpool's Belvedere School for girls, has called on the Government to extend the scheme to the top 100 day schools and - in the absence of an enthusiastic response - has urged other philanthropists to join him. One, Peter Ogden, has announced a pound;25m trust to pay for at least 200 scholarships at 10 leading schools.
But the chances of a national scheme that would really open up access to the country's most academically successful schools seem remote. For it is now selection as much as money that really divides independent schools from most of their state counterparts.
Until a government is prepared to countenance an integration scheme based on selection, breaking down this educational apartheid will remain a pipedream.
"At St Paul's we teach nothing but the classics, nothing but Latin and Greek. If you want your son to learn anything else you must have him taught at home, and for this purpose we give three half-holidays a week."
Sleath, 19th-century headmaster of St Paul's, to a parent, quoted in J Gathorne-Hardy's 'The Public School Phenomenon'
"The year is 1910 - or 1940, but it is all the same. You are at Greyfriars, a rosy-cheeked boy of 14 in posh, tailor-made clothes, sitting down to tea in your study in the Remove passage after an exciting game of football... The king is on his throne and the pound is worth a pound... Everything is safe, solid and unquestionable. Everything will be the same for ever and ever."
George Orwell, 'Horizon', March 1940
"The public schools are not divisive simply because they are exclusive. An exclusive institution becomes divisive when it arbitrarily confers upon its members advantages and powers over the rest of society. The public schools confer such advantages on an arbitrarily selected membership, which already starts with an advantageous position in life. There is no sign that these divisions will disappear if the schools are left alone. They themselves deplore this. It is time we helped them to change a situation which was not of their making."
The Newsom Report, 1968
"The screening out of the sons and daughters of the affluent and influential from the rest of society for their formative years - prep school to university - and the consequent indifference of their parents to what goes on in state schools is more than a traditional quirk in the English system. It severs our educational culture at the neck."
George Walden, 'We Should Know Better', 1996