Shadow schools secretary Michael Gove may have peppered his party conference speech in Manchester earlier this month with suggestions that Labour education policy had failed.

Yet the more one hears the detail of what Gove is planning, the more he seems to be taking Labour’s successful policies and pretending they are his own.

Sometimes, to be fair, he is candid about his admiration for Tony Blair’s schools policies. But he is just as likely to try to exaggerate the differences that exist.

Yet by looking to Labour’s Teach First for a blueprint for his teacher training reforms, he is paying a tribute to changes this government has made.

And, by extending academies, he is recognising the success of a Labour programme that has already helped to reduce the number of low performing secondaries – those where fewer than 30% of pupils get less than five good GCSEs including English and Maths – from 1600 when the Tories were last in power to 270 today, a remarkable achievement by any standard.

Even his plans to allow more parent-led schools or develop chains of like-minded ones will build on legislation introduced by Labour.

There are areas where Labour should have been bolder: Gove will allow primary academies, where currently only all-through academies have primary provision. And he will give outstanding schools the right to become academies if they partner a weaker school, something still requiring government permission, though any school can now easily become a foundation school or trust if its governors wish it.

However, the Tories could face problems if they ignore how Labour has succeeded. That’s why it is no bad thing that they have Sir Bruce Liddington, the former schools commissioner, and Baroness Morgan, who works with Ark, advising their quasi-independent New Schools Foundation.

First, they need to drive demand as well as enabling it to emerge organically. That is the big lesson of academies and trust schools. There is always reluctance to be an early adopter, and it took huge energy by Lord Adonis, Sir Bruce and others to work with schools locally and overcome problems with local authorities. Now, authorities are queuing up for academies.

Gove would be wise politically to stick with his initial instincts and leave the new schools non-profit making, at least until they are established, whatever the Swedish and American profit-making entrepreneurs say. It will be far harder to sell profit-makers politically in a UK environment, with a strong tradition of not-for-profit independent schools than in Sweden, with no such tradition. Moreover, most American states prohibit profit in charter schools.

Second, he must recognise where Labour’s reforms have succeeded. There have been substantial improvements as a direct result of a much more business-like focused attitude in schools – and a big improvement in the quality of teachers. Of course, too many targets can create their own problems. But floor targets – like the 30% minimum five good GCSEs in the National Challenge – and tough internal targets within schools has driven substantial improvement.

Unless the Tories are prepared to overcome their opposition to targets and expect similar ambition, they will not achieve the further boost in improvement our schools need. In the meantime, Labour should welcome the fact that the Tories want to build on our policies. But we should not allow them – or the voters – to forget who introduced them in the first place.