The case of Mrinal Patel, who was accused of cheating to win a place for her son Rhys at Pinner Park primary school in Harrow, is a parable of all that does not work in school admissions. Mrs Patel faced up to a year in jail or a £5,000 fine after Harrow Council brought a case against her for a breach of the Fraud Act 2006.

The legal case has now been dropped and Mrs Patel is adamant that her temporary residence in the school catchment area just happened to coincide with the school admissions process. Whatever the truth of this case, it is unlikely that there are no parents prepared to bend the truth to get the best school place for their child. For example, plenty seem to find previously dormant religious convictions with the prospect of a good church school place on offer. Many wealthy parents are also able, perfectly reputably, to move close to a good school to ensure their child a place. House prices around a desirable primary school command a specific education premium.

As long as there are too few good schools in the state system, and as long as private education remains beyond the budget of the vast majority of parents, disputes such as this one are inevitable. When a school is rated as outstanding by Ofsted, as Pinner Park was, it is bound to be oversubscribed. Parents have a right to express a preference and, not surprisingly, many more chose Pinner Park than can be satisfied — there were 430 applications for 90 places.

In line with common practice the school allocates places in these circumstances by proximity. It draws a catchment area around its site and children who live within are preferred to those who live without. The upshot is that the social pattern of the area is mapped on to the population of the school and the house prices in the immediate vicinity go up, excluding anyone without the required purchasing power.

The best way to avoid repetitions of Pinner Park is to ensure that the second-choice option is always excellent. This means better teachers and less control of the supply of schools. Finland’s system is highly centralised and controlled but its schools consistently perform better than any other nation because its teaching qualification is taken as a signal of high quality by employers. In Sweden, the deregulation of the schools market brought new school chains, many of them profit-making, into education. The boost to supply improved performance overall.

In the meantime, it will be imperative to fix the admissions procedure. The first thing to do is to abolish the catchment area. Schools should give priority to siblings but they should not be permitted to use locale as a criterion for selection. Parents will still be free, of course, to choose their local school but there would be no longer any profit in lying about where you live. Then, in the event that a school had more applicants than places, the allocation should be settled by lottery. Precisely because a lottery is blind, it is fair. Everyone, regardless of income or background, has exactly the same chance of success.

This will take some arguing. Parents who have become accustomed to playing the system to their advantage will not like it at all. But parents such as Mrinal Patel are just responding to the incentives in the system. Until there are more schools and no assumption that proximity is a trump card, this problem will not go away.