There has been so much wildly ill-informed journalistic speculation around the race to be PM, that to add to it might be considered pointless. Irresponsible, even.

But I am on an East Midlands train on the way back to London from the fabulous Hallam Festival of Education and the wi-fi is so shonky that it’s preventing any proper work, so here goes: let’s play a game of Name The Next Education Secretary.

Before we start, two warnings: first, what follows, although based on lots of informed conversations, is hugely speculative and should be treated as nothing more than that. Second, it is predicated on Boris Johnson becoming PM and getting to pick a cabinet (and for the next week or two, we’re always just one “hilarious” gaffe away from that not happening).

Also, I am assuming that Michael Gove would not want a return to the Department for Education, and that Johnson would not offer it to him.

The next education secretary: 'runners and riders'

So who’s in the running for the big office in Sanctuary Buildings if Bojo is handed the keys to No 10 next month?

First up, Damian Hinds, the continuity candidate. He’s hardly set the world on fire in his year or two steering the nation’s schools, but he is still considered a safe pair of hands and might represent stability in these febrile times. In his minus column, Johnson clearly plans to hand the DfE a wedge of cash and so may consider the job a reward for a loyal lieutenant or a big political beast he needs to keep sweet, in which case Hinds makes way.

Next, Liz Truss. Formerly a schools minister, Truss, now chief secretary to the Treasury and a high-profile Boris supporter, is being talked up as a potential chancellor. Should that not happen (Sajid Javed is now believed to be after No 11 as compensation if he drops out), then surely Truss is a frontrunner for next ed sec. Truss likes tests. A lot.

One name that has come up more than once in such discussions is former FE minister Robert Halfon, the current chair of the Commons Education Select Committee. Halfon is a Brexiteer, but out of the "Red Tory", working-class Conservative tradition. His appointment might come as part of an attempt to build a cabinet in the style of a broad church. He’s very, very big on skills.

One current runner and rider in the leadership race, who might expect a big role in a Johnson administration, is health secretary Matt Hancock. There would have to be a reason for him to be asked to leave the Department for Health, but if the former FE minister is moved then education seems logical enough. If that were to happen, you’d have to brace yourself for a renewed focus on edtech. Apps all round.

In the same kind of category we find Rory Stewart. Such an appointment would be dependent on Stewart not doing exceptionally well as the battle to be leader develops, but well enough for him to demand a bigger gig than the Department for International Development. It is also predicated on his willingness to serve under Boris (unclear: the aforementioned wi-fi isn’t allowing me to check) and him not replacing Jeremy Hunt as foreign secretary, which would seem his natural berth.

And then there is a name likely to scare the horses. I have to admit that this is my own, wild speculation: Gavin Williamson. The apparently disgraced former defence secretary has clearly hitched his rehabilitation on the Johnson bandwagon, taking up an unofficial, but senior, role in the campaign. If this is to be rewarded with a return to cabinet, which is a reasonable assumption, then where? He’s certainly not currently in receipt of the levels of personal capital or respect required to be given one of the Great Offices of State (chancellor, home or foreign secretary), so why not education secretary? After all, the DfE is hardly awash with state secrets for him to give away…

Obviously, there is every chance that none of this will happen: there’s a lot of political water to yet rush under the bridge. We are also yet to be certain what priority schools are likely to have under the new administration.

In addition, there have been an unprecedented number of candidates running for the leadership and Johnson may well want to give most of them big gigs to keep them inside his cabinet urinating out (to paraphrase Lyndon B Johnson). So, what price Andrea Leadsom or Esther McVey?

And if Johnson were to throw it all away in some gaffe-inspired death spiral, what about the blond bombshell himself? After all, he couldn’t be chancellor or home secretary (those require a degree of interest in details and mundanity that have hitherto escaped him) and those with long memories will remember that he was once a shadow HE minister…

You have been warned.