But coping with the linguistic needs of these children and the disadvantages of the homeless, and delivering the national curriculum to children in those schools where the average stay is less than a year, appears trifling in comparison with the main challenge - finding enough experienced teachers to match the increase in pupil numbers.
What will load the dice against London is that it is by far the biggest net exporter of teachers in England and Wales. Its concentration of teacher-training institutions churn out far more new practitioners than the capital needs. On leaving college many of them decide to look for jobs in London and go on enjoying the metropolitan buzz for a bit longer. But when they think of setting up home, the capital's house prices and the high cost of living often force them to move to schools in the provinces.
The fact that the school population is rising all over the country, although only half as fast as in London, means that it will become much easier for the newly qualified as well as experienced teachers to move out.
As yet the all-London figures for teacher vacancies give no hint of an approaching crisis. Last year, the latest for which official figures are available, there were said to be 474 unfilled posts in the whole of Greater London, little different from the vacancy rates for the previous four years.
But unpublished figures from the Department for Education and Employment suggest that this may not be because teacher supply is matching the rise in pupil numbers. Schools, it appears, have taken on hardly any extra teachers despite a huge rise in pupil numbers.
If this is true for the country as a whole then its effect in London could be more damaging because of the faster rise in pupil intakes. Heads and education departments say that, in any case, the overall London vacancy figure could be providing false reassurance. Schools in certain localities are finding it increasingly hard to attract applications; and that, say veterans, is the way the London recruitment crises of the early 1970s and the 1980s began.
ILEA launched massive recruiting drives to overcome those shortages, including bringing in teachers from overseas - and even in recent years, many of London's primaries have relied on Australians and New Zealanders - most of them impressively competent practitioners. The vast majority of these backpacking teachers have been supplied by agencies who are plugging an estimated 1, 000 staffing gaps in inner London schools each week.
The boroughs think that a London government could not only organise recruitment drives but, more usefully, persuade the Government that it must fund much higher weighting allowances for London teachers. At present even some charities offer a bigger London weighting allowance than teachers receive.
But borough politicians who have studied the pattern of teacher supply over the years could be praying, party loyalty notwithstanding, that the former chancellor was right in predicting economic gloom and doom under Labour. Unemployment is the best recruiting sergeant the Army has; and the same rule applies to teacher supply.