One Conservative leadership campaign is active in Portcullis House, the annexe to parliament where MPs and journalists mingle, sharing tea, coffee and (in my case) Danish pastries.

Jeremy Hunt’s supporters are promoting him as the answer to the party’s (and the country’s) problems. He has cabinet experience but is untainted by the alleged low moral tone of the Boris Johnson administration. He ran an impressive campaign last time, when the need for a bullish norm-breaker meant the party turned to Johnson to get Brexit done. And he has been gaining ground a little in the betting markets as gamblers adjust to the collapse of Rishi Sunak’s prospects.

In a wide-open field, he, Liz Truss, the foreign secretary, and Tom Tugendhat, the chair of the Foreign Affairs Committee, are vying for the misleading status of “favourite”, yet none is given more than a one-in-seven chance of winning the race.

I wrote last week about the difficulty of beating “somebody with nobody”, which is why I think the chances of Johnson being ejected from office are lower — or, rather, later — than some of the excitement of the past week has suggested.

When he is eventually turfed out, I don’t think any of those three will replace him. They are all Remainers, and the Leave-Remain divide is still the most important identity marker in British politics. This is especially true among Conservative Party members, who have the final say over who shall be leader.

Which is why the undeclared leadership campaign that is more interesting than Hunt’s is the one being fought by Michael Gove. It takes the form not of supporters whispering in the ears of journalists by the indoor fig trees of the Portcullis House atrium, but of a cabinet minister doing things. Gove was drafted in to get the Homes for Ukraine refugee scheme up and running when the Home Office seemed to be trapped in bureaucratic inertia. It is more up and stumbling, but at least it is happening, slowly.

Then Gove announced a breakthrough in negotiations with the big building companies, who agreed to pay for replacing dangerous cladding on high-rise blocks of flats. It is now five years since the Grenfell fire, but finally Gove has delivered what leader writers have been demanding all along. A leading article in his old newspaper, The Times, praised him to the skies.

Last weekend, he scored another direct hit, with a headline on the front of The Sunday Telegraph: “Gove’s £7bn developer levy in line to boost council housing.” Instead of requiring builders to allocate a proportion of new housing to “affordable” homes — contracts that are often contested after the event — he is proposing legislation in the Queen’s Speech next month to impose a levy on the companies which would then go to local councils to build social housing.

The “council housing” line is classic Gove (although I realise that it might have been The Sunday Telegraph’s phrase): it is what a lot of people think we should have more of, even if it is all built and managed by housing associations these days. Just like the time when as education secretary he proposed to “bring back O-levels”. He’ll be legislating to restore Marathon bars and Opal Fruits next, and then he will lead a campaign to bring back galleons, sickles and knuts.

He has a good feel for populist bring-backery, which is, after all, much of the sentiment behind Brexit, but he is also such a left-wing centrist that he is an honorary Blairite. At education he finally tranquillised the Tory party’s grammar-school tendency with a commitment to academy schools as the route to equal opportunity. In his brief tenure as justice secretary he started an enlightened prisons policy that sadly hasn’t been followed through. But now at the Department for Levelling Up, Housing and Communities, he is striking out on another great egalitarian cause.