A few months after Nicola Sturgeon became First Minister she spoke approvingly of something called the “London Challenge”.

The SNP leader even visited Blue Gate Fields junior school in London’s Tower Hamlets, now ranked in the top 20 per cent of English schools for attainment in grammar and reading, and the top 40 per cent for maths.

Quite a turnaround from when it and many similar inner-city schools – memorably dubbed “bog-standard comprehensives” by Alastair Campbell – were among the worst in the country.

Ms Sturgeon was doing a number of things with that visit and accompanying comments, demonstrating she was willing to “think differently” and challenge educational orthodoxy. She even borrowed its nomenclature by launching the “Scottish Attainment Challenge” last February.

This was broadly welcomed, as was her broader acknowledgement of problems in Scotland’s schools, not least the ever-widening attainment gap within the state sector (private education remains one of the Great Unmentionables in Scottish politics), a long-overdue break with the dominant, and intolerably complacent, “Scottish education is the best in the world” mantra.

Last week the Scottish Government launched a new National Improvement Framework, which will co-ordinate national assessments for primary school pupils. These will be piloted this year before being rolled out across Scotland in 2017, testing reading, writing and numeracy in P1, P4, P7 and S3 to evaluate pupils’ progress.

As a breakdown of Scottish exam results in 2015 has shown, the attainment gap between the richest and poorest pupils has widened again. Now of course testing will not, in itself, reverse (or even halt) that trend, but it will make it much more visible, although as Judith Gillespie (formerly of the Scottish Parent Teacher Council) pointed out in these pages a few days ago, there is a risk in all of this of data-fuelled inactivity.

In other words, we already know children who come from disadvantaged backgrounds won’t perform as well as their counterparts from more affluent areas, and we already know – even without standardised testing – that their exam results will be worse. So the upshot, as Ms Gillespie concluded with obvious frustration, will be an educational system going “round and round all over again to establish precisely the facts we already know, and still nothing will actually be done to rectify the problem”.

Don’t get me wrong, data is important, but there is a horrible tendency to believe it’s an end in itself. Although an important part of the London Challenge was data, not only about each school in general terms, but about the performance of individual subject departments and of students from ethnic groups (a high proportion in London boroughs like Tower Hamlets), key was its subsequent use.

According to Sir Mike Tomlinson, a former chief adviser to the London Challenge, accumulated data was used to create “families” of schools with common characteristics, meaning schools could not defend often bad performances by arguing that their needs and challenges were somehow different from other schools: there was no place to hide.

Tower Hamlets was particularly ambitious in this respect, engaging with its Bangladeshi community on education issues and using data and statistics to track their pupils’ performance. Cash and leadership was also important: if the London Challenge succeeded it was due in part to it being almost a moral crusade, a collective professional commitment to improving the city’s schools across the board.

I use the qualification “if” because there is research that suggests the London Challenge built upon – rather than sparked – a remarkable turnaround in the city’s schools. By 2005, for example, most London schools had already risen above the national average, the Challenge having been launched just two years before.

There was, in other words, no single explanation: rather, gradual improvements in primary schools since the mid-1990s, including school inspections, choice and competition, had all played a part, as had the abolition of the Inner London Education Authority in 1990 (opposed by Corbynistas of the day), which transferred control of education to individual boroughs.

As the academic Tony Travers writes in a new book, London’s Boroughs at 50, it was at around this time a demonstrable shift in local authority leadership took place, particularly in Hackney, a part of the city I know well. In the 1980s Hackney was a byword for failed government, and in 1996 the local Labour Party was so riven with factionalism it proved incapable of forming a functioning administration. The borough, said one resident, was “Britain’s North Korea. It’s the place modern politics forgot.”

Then things began to change: in 2000 a new chief executive was installed to get a grip on Hackney’s chaotic government, and in 2002 the council adopted a directly-elected mayor model. Education was key to its transformation, with Ofsted now ranking every secondary school and most primaries as “good” or “outstanding”. “More than any other borough, and faster,” writes Travers, “Hackney turned from being a governmental basket case to a model council.”

And its success had little to do with dogma, particularly in the field of education, where increased choice, competition and autonomy have all played their part. Here I suspect Scotland, or rather the Scottish Government, is likely to make less progress than in the UK Capital – however hard it tries to emulate the London Challenge – for policy debate in Scotland deems so much to be off limits that coming up with something genuinely radical is all but impossible.

So last year, when the First Minister was making otherwise positive noises about Blairite education policy, she was also careful to make it clear she had “no truck with the ideological nonsense of Michael Gove and the Tories”, ie no truck with academies, competition or any of the stuff that research suggests has helped transform London’s schools. And while the jury’s still out on the extent to which the Blair/Cameron approach to education reform has made a difference, the lack of dogmatism has at least enabled debate and change, much of it good.

Helpfully, the Conservatives in Scotland are finally moving beyond tired old policies like education “vouchers”, floated by everyone from Michael Forsyth to Ruth Davidson as the means by which to achieve an educational revolution. Instead a recent paper set out three “stepping stones” focusing much more on autonomy, management and recruitment.

Combine that with massive extra resources (the £100 million budget of the Attainment Scotland Fund is welcome but not nearly enough) and targeted staffing in disadvantaged areas (“Teach First” has been controversial but effective in England), and Scottish schools might become the next educational success story.

Tinkering won’t cut it, and nor will standardised testing, but if London, with its relatively weak devolved Assembly, and boroughs like Hackney and Tower Hamlets, which have a fraction of the power and cash possessed by the Scottish Government, can manage it, then undoubtedly so can Scotland.