Heavy weekend? You and Boris Johnson both. The Foreign Secretary is nursing one hell of a hangover after he kick-started his Friday evening with a couple of Jägerbombs and a 4,200-word article for the Telegraph laying out his vision for Brexit. As one does with an article that is categorically not a leadership bid, he put the whole thing on his Facebook page in order to circumnavigate the Telegraph's paywall.

In the article, he did three things. The first was to re-open the row over that £350m bounty for the NHS, earning a sharp rebuke from the head of the UK Statistics Agency, David Norgrove. "Johnson in 'distortion' row after £350m Brexit claims" is the Guardian's splash while "Number-crunchers take Johnson to task over revived £350m pledge" is the FT's.

The second and more important aspect as far as the Brexit process goes was to set himself against continuing payments to the European Union after we leave, a stance which, if committed to by the government, would necessitate an immediate exit in March 2019 with no transition and a significantly worse standard of access to the single market than the one we currently enjoy.

But Johnson has been left isolated after the Cabinet's big beasts – not Amber Rudd or Damian Green, as you'd expect, but also Michael Gove – declined to back the stance. That any final deal will be the choice between May's deal-with-payments and an exit without will mean that any Brexit ultras who rebel will surely be outnumbered by opposition MPs doing what they can to avoid a cliff-edge Brexit. "Johnson cut adrift after Brexit ploy backfires" is the Times' splash.

The decision to relitigate the £350m row tells you a lot about the Foreign Secretary. There's a reason why some Remainers obsess over it: it was a politically effective deception that they failed to counter. But almost alone on the winning side, Johnson is incapable of shrugging his shoulders and saying, yes, it was a lie, but that's politics for you. As Francis Elliott explains in his excellent analysis of the whole row, Johnson's bruised feelings about the £350m for the NHS as well as a sense that he was being cut out of the Brexit talks drove his unexpected intervention.

The third thing Johnson did of course was re-open the discussion of life after Theresa May. As far as SW1 goes, it's Amber Rudd who is in pole position – she used her appearance on Marr yesterday to remind viewers of her credentials as a steely operator, accusing Johnson of "back-seat driving" and adding that she hadn't read the piece as she had "rather a lot to do" responding to the terror attack at Parsons Green.

It's certainly true that Rudd is the candidate that Labour would least like to face and the only Cabinet-level successor to May that generates any spontaneous enthusiasm among MPs. It's also true that, on the whole, Johnson has strengthened rather than weakened the fears that MPs have about him: that his vanity and poor sense of timing make him an ill-suited replacement to the PM.

There's a big "but", though, which is that precisely the reasons that Rudd worries Labour and is well-thought of in Westminster make her vulnerable among Conservative members. It may be that the real golden ticket in the next Tory leadership race is whoever can come second, and with that face Rudd among ordinary Tory members. And that second-place could, still, end up being Boris Johnson's.