There is reason to believe that most schools will open for the start of the new term – if not all at once, at least early in September.  This is because parents are more responsive (hopefully and the unions less obstructive (certainly).

First, parents.  It may be that the fall in Coronavirus hospitalisation and death numbers; the coming end of furlough; difficulties in balancing working from home with caring from home; and, above all, a creeping realisation of the damage that non-schooling does to children’s life has cut through.

Second, unions.  It looks as though a shift in parental opinion, and that the apparent fall in the lethality of Covid-19, has had an effect.  The NAS/UWT says that the statement issued by Government medical officers “adds weight to the Prime Minister’s message that there is a moral duty to reopen schools”.

Even the National Education Union is now advising union representatives “to seek meetings with school leaders in order to discuss plans for full opening”.  So there is a plausible case for believing that the political damage done to Gavin Williamson, who can’t now be an effective spokesman for re-openings, won’t substantially delay re-openings.

Proof that Downing Street believes that his reputation among parents is shot comes in the form of Boris Johnson getting out on the front foot and taking the communications lead.

“It’s vitally important that we get our children back into the classroom to learn and to be with their friends. Nothing will have a greater effect on the life chances of our children than returning to school,” he says today. And Number Ten seems to have grasped the message that what’s needed now is a strategic communications plan.

Part of such a plan for any Government is the recognition that politicians aren’t the best-placed people to convince sceptical voters.  In this case, Downing Street gets it – quoting a statement from Chris Whitty and the other chief medical officers.

“We are confident in the extensive evidence that there is an exceptionally small risk of children of primary or secondary school age dying from COVID-19,” they now say.

This is a welcome shift of gear.  You may not trust the medical officers, but many people will do so – more than they will the Government’s Ministers, anyway.  But the Prime Minister is not out of the educational woods, and Williamson is in no position to help guide him.

For what happens if the Coronavirus returns during the winter, death numbers and hospitalisations rise, local lockdowns intensify, and many workers are confined to home?  Or if, heaven help us, there is a second national shutdown (to which we are opposed if, as is now the case, the threat to the NHS is remote).

In these circumstances, pressure will grow to close schools, most likely on a local, area or regional basis.  It is hard to see how they will function if teachers in certain areas are locked down.

And parents may start keeping their children at home in any event. In these circumstances, Number Ten will need to act more energetically over online learning than it has done to date.  The quality has been very patchy – with the private sector outperforming the public.

There will always be a need for face-to-face teaching in education, and younger children must learn how to socialise.  But online learning is a growing presence, and Covid-19 will speed it up.  Ministers should be looking at Tom Tugendhat’s ideas for helping to fund parents to buy teaching online.

In these circumstances, Downing Street will also have to dust down its fledgling communications strategy.  Mobilising scientists is good, but deploying teachers, parents and educationalists would be even better.

Michael Gove reached a similar conclusion in Opposition, as he contemplated the push by John Patten, Education Secretary under John Major, for school opt-outs from local authority control.  It faltered, together with plans for curriculum reform.

Patten had worked top-down and Gove, on academisation, worked botttom-up, at least in part – by encouraging the free schools movement, and legislating to assist it.  If the Government runs into schools trouble this winter, it will need to mobilise voices who can put the social justice case for pupils getting to school with passion and expertise.

These should include inspirational teachers, such as Katharine Birbalsingh.  Plus school providers, such as Ark; or not-for-profit organisations such as Parents as First Teachers.

“One mum on Mumsnet is worth a hundred Ministers,” one adviser told ConHome. Number Ten, rather than the Education Department, will have to take the lead if a crisis arises, if only because Williamson is unlikely to be in a position to persuade non-MPs to pitch in.

And when it comes to strategic communications, Downing Street could learn more broadly from the Treasury, in any event – now. Rishi Sunak’s popularity won’t last forever.  But he is effective not only because he is giving people what they want (currently), or because he is a crisp, well-briefed and direct interviewee.

Never mind, for a moment, the cute graphics, with his signature on them; or the photo of a young, dynamic Chancellor beavering away at his desk, wearing a hoodie.

More to the point, his team have developed an way of packaging their offers.  So schemes designed to help business access money more quickly are “bounceback loans”.  Sunak’s plan to boost the hospitality industry is “eat out to help out”.

Were other departments as disciplined in their communications, Ministers would govern more effectively.  Meanwhile, the Government will need to clear the airwaves and studios for women Ministers, such as Vicky Ford, since mothers will be a key target audience during the coming weeks.