Labour should be unbelievably popular with teachers right now. School budgets are shot, which led to an unprecedented protest by headteachers. Teacher retention is at a record low and the government has missed all recruitment targets for five years. Secondary school places are in short supply. And yet, in a recent survey of more than 2,500 teachers, fewer than half said they would vote Labour if an election were called tomorrow.

Admittedly, just 9% of teachers said they would vote for the Conservatives. But if Labour can’t confidently secure half the profession’s votes it has a real problem, because the party relies on public sector workers to boost its popularity in a way the Conservatives never have.

So, what is Labour’s problem? The so-called National Education Service is the linchpin of the party’s planned fightback – but no one knows what it means. In part, that’s because Angela Rayner, the shadow education secretary, isn’t being allowed to develop it properly.

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Over the summer she ran a series of public meetings to work out the details of the policy. At the launch of the consultation, Corbyn turned up – shaking hands, kissing babies. It’s hard for Rayner to run a serious policy forum when participants are queuing up for selfies with Corbyn. To some of us, it looked like a panicked leader worried by the growing popularity of a junior.

On top of this, Rayner has other issues to contend with: John McDonnell promising bizarre things, such as refusing to pay the private companies who run some school buildings (good luck with the legals on that); the financial burden of Corbyn’s promise to make university free (seen by many as an enormous transfer of wealth to the middle class). And a continued hokey cokey over academies: are they coming back into local council control or staying out? No one knows.

Teachers are battle weary and their appetite for more big reform is low. If the Conservatives were to lift austerity as promised and put a cash boost into schools, while promising to change little else, this could seem appealing. May’s team has also pulled back on free schools and put aside money for mental health programmes. Teachers may not like what they are getting with the Conservatives, but at least they more or less know what it is.

The education secretary, Damian Hinds, is leaning into the situation. Last week he attacked Corbyn’s “control freakery” and said giving schools back to councils would mean putting politicians in charge, rather than headteachers. It’s not a fair statement, but in a world where people are fed up with politicians, it’s a canny one.

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Relying on the Conservatives to make the same mistakes as in the last election would be a fool’s errand. Money will be conjured up just in time for voting; grammar schools will be hidden in a weasel-worded policy about “allowing selective schools to expand”.

Labour needs to get wise. If there is a general election in the offing it will be hard to go to the polls offering unrealistic sums of cash for an amorphous set of revolutionary-sounding ideas. Teachers are too tired. Parents will find it confusing.

The National Education Service needs to be as simple as possible: free childcare, a good quality school place for every child, subsidised university and workplace learning for all. Simple to understand, if horribly complex to deliver. But that’s grown-up politics for you.

In the end, teachers and parents of school-aged children are a huge political opportunity. There are 12 million of them. If Labour can win their support, the party has decent prospects in a future election. As it stands, votes are going spare and the Conservatives are on a hunt to catch them.

Rayner has the right instincts to fight Hinds, but Corbyn needs to stand back and let her fly. A future election may depend on it.

• Laura McInerney is the chief executive of Teacher Tapp and a governor and former teacher at a London academy school

• This article was amended on 17 October 2019 to clarify that Jeremy Corbyn appeared at the launch of Labour’s education policy consultation.