No general election has ever been decided by the voters’ verdict on a single issue. Education is no exception. Yet political leaders have sensed that next time round the electorate’s assessment of their education policies could tip polling-booth decisions. If they are right, the picture which emerges from a recent series of ATL-commissioned Harris polls may provide the best current evidence of where voters’ crosses will go. That voter profile also maps the political terrain which the winning party must capture as the election campaign heats up.

For Tories, the present situation must seem all but disastrous. Public assessment of the Government’s education reform programme is that it has been either ineffective or a downright flop. Just over one in four voters believes that it has done nothing to raise quality, and almost half (41 per cent) conclude that it has made things worse.

Only one in five voters believes that a post-election Conservative government would be the best party either for raising the quality of education, for getting the best out of teachers, or for investing more in schools. Given high public anxiety about unemployment levels, the merging of the Education and Employment Departments could well backfire, since a mere 17 per cent of the electorate are currently convinced that Conservatives would offer the best job prospects for children at the end of their education. That is not merely gloomy news for Tory supporters generally. It is an ominous message for Gillian Shephard personally, now in charge of the whole shooting match.

For a government which has invested so much credibility in its claim to be improving state education, it is ironic too that a majority (admittedly small) of those polled believes that parents who want to jump ship and send their children to independent schools should get more financial support. That majority is most clear cut, at 53 per cent, among C2 voters, the very socio-economic group which may be crucial to the outcome of the next election. But Tories interpreting that C2 instinct as vote-winning support for expanding the assisted places scheme should be wary. Those who would have to subsidise any expansion most - higher-earning AB and C1 voters - are positively opposed to it. The Labour commitment to phasing out the scheme entirely has done nothing to trim their poll lead, with most voters (including the C2s) believing that independent schools would be safe in Tony Blair’s hands.

Mrs Shephard has been credited with arguing in Cabinet that what might have been a Conservative success story risks turning into a ghastly nightmare. If she did, she was dead right, and Prime Minister Major and Chancellor Clarke will ignore her at their peril. If she either didn’t argue the point or, perhaps even worse, did so but lost the day, then Liberal Democrat Don Foster’s cheap but barbed conference jibe about her being the Miss Helpful who ended up helping no one will prove all too true. That outcome could cost her and her parliamentary colleagues the next election.

But how would the electorate react to the policy with which John Major is rumoured to be flirting most heavily - the compulsory opt-out of all schools into the publicly-funded quasi independence of grant-maintained status? On current evidence he should forget it. Fewer than one in five voters is in favour, and 60 per cent are positively opposed (with clear majorities against in every voter category).

Yet this apparently decisive thumbs-down to a government on the ropes may point, particularly when seen in the context of other ATLHarris poll findings, to a key issue over which the electorate seems confused, but could yet be swayed by the party which gets on to it fast enough.

On the opt-out issue, a quarter of those polled were “don’t knows”. So although post-Brighton Labour - particularly after Roy Hattersley’s lightning conductor conference speech - may be relieved that a slim majority of voters believes that they would treat opted-out schools fairly, Messrs Blair and Blunkett should take no comfort in the fact that one in five is still uncertain.

They should also worry that nearly half the electorate is unconvinced that a Labour government would offer parents as much choice in education as the Conservatives. Nor should they overlook that, though well ahead of the Tories, less than half the voting public yet believes that they would raise standards, motivate teachers or guarantee youngsters employment.

This voter uncertainty is reflected in other poll findings. Asked, for example, whether local authorities should be less involved in running schools than at present, intriguingly the jury is hung. Half the electorate says ‘No’ - but 39 per cent favour even more LEA disengagement, and 11 per cent are undecided.

Possibly that uncertainty takes us to the centre of an important pre-election debate which has yet to get seriously under way. Beyond the rhetoric about local democratic accountability as against the cost of inefficient town hall bureaucracy, just what are the main political parties saying about the future of local government?

Men and women on top of the Clapham omnibus are unclear, and I don’t blame them. Local management of schools, and more governor and parental involvement, have increased the public’s feeling that schools are essentially community assets. They have heightened voter wariness of rough justice decisions from the centre which, however well-intentioned, override or are insensitive to the priorities of the local schools which parents use. They see the push for school improvement as much a community issue as a Whitehall-driven imperative. Smarter local authorities have got the point. The main parties nationally have yet to wake up to it and spell out their plans with any clarity.

Take the issue of rising class sizes. Conservatives and their trusted advisers can talk about the unimportance of the issue until they are even bluer in the face. The public simply does not believe them. Nearly 90 per cent think that any class of more than 30 pupils worsens discipline problems, almost 95 per cent believe that the more personal attention a child receives from a teacher, the better.

More than 90 per cent would support teachers who took protest action, and a startling 23 per cent would support strikes. Tony Blair was therefore spot on to realise the importance of the issue, but he must now persuade the public that a Labour government would honour his public commitment and fast. That will mean coming up with a costed plan which convinces an electorate disposed to be cynical about all parties, including his.

What role might LEAs play in this or anything else? As things are, it is possible to define the role of post-election LEAs, whatever the outcome, only by negatives. They will be responsible for discharging statutory duties which no government has the appetite to repeal. They will take on what neither government wishes to afford nor individual schools can pay for unaided. And what is more, they are promised a strategic role. Claptrap. The truth is that they will have accountability without means. They will have responsibility without power - the prerogative of the eunuch through the ages. It simply won’t do, and Sir Malcolm Thornton was absolutely right in last week’s TES to make that very point.

Beyond conceivable doubt, voters want to see standards rising. They see improved national investment as part of the answer. Nearly 80 per cent of all voters - and just under 90 per cent of those with school-aged children - would support the Liberal Democrat policy of a penny more in tax for education (although only 55 per cent believe that such a government would actually spend more).

But they also see schools as local assets, not mere Department for Education and Employment customer outlets. And they are looking for more than manifesto semantics to convince them that the next government really understands that.

Peter Smith is general secretary of the Association of Teachers and Lecturers