There are so many reports published about various aspects of education that it is hard to distinguish the truly important from the merely interesting and the outright irrelevant. The document issued by the National Audit Office (NAO) is, nonetheless, without doubt, a serious investigation that merits special attention. Although ministers can point out that the number of schools deemed to be failing or underperforming is falling, the NAO estimates that there are more than 1,500 schools — mostly in the secondary sector — that are producing unacceptable results. This conclusion is not challenged by the Government.

In an ironic fashion, however, the bad news is good news for the Prime Minister. There are many on his own backbenches who do not see any pressing reason to “fiddle further”, as they would put it, with the structure and organisation of schools. They would prefer that ministers let matters be and allow the extra money spent on education to have its benign impact without making the structural changes necessary to secure that outcome.

The status quo is not satisfactory. The NAO rightly praises the work of Ofsted, but urges those who inspect schools to focus more intensely on problem cases and become more demanding of institutions that could not fairly be described as “failing”, yet are at risk of institutional mediocrity. This is sound advice that the inspectors are apparently heeding. But there are limits to the extent that Ofsted by itself can raise standards. The character of schools matters most of all.

That is made plain by the NAO in its assessment of the common traits of underperformance. These are ineffective leadership, weak supervision by governors, poor contacts with the world beyond the school itself, and local authorities that only become concerned about failure in a school after that weakness has become manifestly obvious. All these factors combined produce both inadequate teaching and poor pupil behaviour. It is precisely these areas that, at least in principle, the reforms outlined in the White Paper on education last year are designed specifically to address.

What may disappoint ministers the most about these findings, though, is the difficulties that schools have in finding the ideal calibre of head teacher. The numbers of appropriately qualified individuals applying for these crucial posts is, the NAO asserts, “generally falling”, despite often substantial salary increases. In an astonishing statistic, it appears that in 2004-05 “28 per cent of primary and 20 per cent of secondary schools had head teacher vacancies”. A curt two-word summary of the NAO’s numerous detailed arguments is that “leadership counts”; the absence of actual leaders is shocking.

Leadership at the Department for Education and Skills matters as well. The White Paper is a minimum plan for overdue change: it must not be diluted further. It should be a popular package with parents, MPs with an interest in local schools, and the head teachers who would secure new freedoms under these proposals. It has not been well sold. Ruth Kelly, the Education Secretary, is now said to be “safe” despite a Cabinet reshuffle expected shortly. She is a talented administrator, but the task to be faced demands cunning in Westminster and a lot of charm elsewhere. She will have to be more savvy politically to ensure that the necessary reform of schools is enacted safely.