Postcodes are closely correlated with parental income, class and ethnic background. Some parents buy houses in the catchment areas of “good” schools, as defined by test and exam results. Because such houses tend to be expensive - and, according to estimates, at least 12 per cent more expensive if there’s a popular school nearby - only the affluent can afford them.

Given the links between social class and attainment, their children will further boost a “good” school’s results, making it even better, and so able to attract more affluent parents. The system is a formula for maximising social segregation, as well as accentuating the racial segregation which so concerns Trevor Phillips, chair of the Commission for Racial Equality.

As long as this lottery exists, pressure will grow to extend various forms of selection, perhaps to the extent of restoring grammar schools nationwide. Many say this is the only way to increase social mobility. They are mistaken. But that isn’t the point. The present system isn’t working and we have to find a better one.

The answer is to hold a genuine lottery. Parents of 11-year-olds would list their preferred schools (probably six) in rank order. Where first preferences exceed its number of places, every application, regardless of geographical proximity, goes into a hat (or machine) to decide the lucky ones randomly. The unlucky are then allocated to their second-choice schools, where these still have vacancies. Those whose second-choice school is already full, or who lose in another draw, go to their third preference.

And so on.

Except perhaps in rural districts, catchment areas would be abolished. So would a school’s power to select pupils on academic, social or religious grounds, either overtly or covertly. The lottery would apply nationally, so parents need no longer worry about a plethora of admissions authorities with different rules.

In the past, ministers have shown no enthusiasm for a lottery. But there are some signs of change. One of London’s most popular schools, Haberdashers’ Aske’s Hatcham College, has adopted “random allocation” for half its admissions. The National Confederation of Parent Teacher Associations has thrown its weight behind the idea. And Philip Collins, who, as director of the Social Market Foundation, produced a report advocating a lottery, is now a Downing Street adviser.

The admissions lottery has three decisive merits. First, unlike the present admissions system, it is transparent. Parents would continue to be disappointed, but at least they would understand why. Second, the lottery preserves parental choice. I am sceptical of the merits of choice but politically, I fear, there is no going back. Third, the lottery offers the best hope of achieving, in every school, something near a “balanced intake”, with a cross-section of children of different abilities and different social and ethnic backgrounds. Average attainment would rise because fewer schools would be weighed down by a concentration of deprived or low-ability pupils.

The overwhelming advantage of this lottery is that, unlike the postcode lottery, it is blind to social class and largely immune to parental influence. No doubt poorer parents would need encouragement to apply for “good” schools in distant areas, perhaps with offers of transport subsidies. No doubt, too, the middle-classes would still find ways of manipulating the system and statistics professors, who could work out the odds of success as they filled out their preference forms, would be at a particular advantage. But support for the comprehensive system is being slowly eroded, with some commentators and politicians even on the anti-Blairite left turning against it. A lottery may be the last chance to save it.