I hate reviews that give away the ending. But a serious and detailed examination of Labour's record is perhaps the one kind of book where you would forgive me for doing so. Polly Toynbee and David Walker conclude with a question: "Why not much, much more?" This is the right question. The Labour government fell short of its potential. But The Verdict gets to the wrong answer about why that was.

The authors say that Labour was at its best when it was giving more money to public services, but interfering less in how they should be run; that Labour's first term was its best but that "this was a government without much of a sense of direction after 2001"; that New Labour thought that progressive policies had to be "offset by populist Tory gestures on choice or 'reform'".

On all three points, the opposite is true. The book is extraordinary for the range of areas it covers and its encyclopaedic completism, and impressive for not shying away from evidence that doesn't support the central thesis. But that very honesty is what ends up revealing that, far from having achieved much, despite its obsession with reform, the Labour government achieved most where it reformed most.

Health best demonstrates this. Walker and Toynbee summarise the verdict by saying that "what mattered was money", and that the absence of reform in Scotland and Wales showed "how little Labour meddling mattered to patients". Yet later, they make clear that waiting times fell in England by 12 days more than in Scotland, and around 55 days more for those who had to wait longest. They say "that was a difference but was it really worth all the fuss and political antagonism?" To which, I semi-screamed "yes", shocking the other passengers on my train.

They claim that competition damages quality, yet say that "competition had fostered better management". They record that independent treatment centres helped abolish waiting lists, and patient satisfaction reached its highest level since 1984, but still it seems as if it would have been better if Labour hadn't reformed.

New Labour didn't pursue choice or reform choice because they were populist, or indeed Tory. As Tony Blair once said  it's much worse than that, we did it because we believed in it. We believed in reform, not least because it reduced inequality. Schools had been left unreformed in Britain for generations, and generations of young people had had their lives ruined by a system that explained away the numbers who left without being able to read.

Toynbee and Walker are generous about Labour's record on education. They note that the average school performance in 1997 had become the bottom marker by 2009, and that the number of failing schools had dwindled. Far from choice vying with equality, a set of reforms that included choice had reduced one of the worst causes of inequality in Britain.

Rather than saying that reform didn't matter, a better criticism would be that Labour didn't know which reforms mattered. We started off sticking to Tory spending plans before splurging money. Targets were replaced by choice, all the while confused by circular reorganisations (their story of the public health director for the South West who has been in the same job since 1994 but had to reapply for his job seven times between 1997 and 2005 sent shivers down my spine).

Step back from the pixels and the picture seems clear  public services need a combination of investment and judicious reform. Reformers have a range of tools (targets, central diktat, choice, competition, higher pay, professionalisation) and should combine them judiciously.

But to think that those reforms were carried out for perception's sake is to misunderstand New Labour, as is the argument that the government lost its ideological direction after 2001. The first term was full of achievements, such as devolution, the minimum wage and the numeracy and literacy strategies. But this was also the term of rolling back choice in health, deregulating the City and devolving power to London, Cardiff and Edinburgh but not letting them choose their candidate  the ideologically confused term.

Tony Blair became much clearer about his ideology after 2001  whether about intervening abroad, choice in public services or reform of pensions. I suspect that what the authors really mean is that they disagreed with him.

The answer to their "why not more" question is not that we reformed too much. It is that by the time we had worked out how to reform, we had relegated some of New Labour's best founding insights. Pre 1997, education was to be our first priority; by the second term, it had been overtaken by health. Pre 1997, we were pluralists, and tempted by electoral reform; by the second term, we were neither. Pre-1997, we did everything to be seen as prudent; from the second term onwards, we frittered away that reputation for fiscal conservatism.

This is a book that I am really glad has been written. It is a joy to find journalists who want to engage with the substance rather than the melodrama. Inevitably, that means that some chapters are written in prose rather than poetry; what is true of governing is also true of writing about governing.

But in leaving out the divisions of New Labour, Toynbee and Walker under-emphasise the reason Labour fell short of its potential: the division between the principals, which meant that disagreements were fudged rather than resolved, and that the government had too many half-pursued priorities.

Yet what also comes across is a country transformed. Drug use and child and pensioner poverty fell. Gay people could adopt, marry, share pensions. Crime fell. Education and health got better. Britain was diverse and creative. Labour fell short of many self-imposed targets. We lost the election and that's the verdict that most matters. But the lesson of what went best is that it happened when we were at our boldest.

James Purnell was MP for Stalybridge and Hyde from 2001 to 2010. He is chair of the Insitute for Public Policy Research.