Here is a one-question quiz to find out if you are a member of the Out Of Touch Liberal Elite: is Boris Johnson a buffoon who makes Britain a laughing stock in the world? If you say yes, welcome to your premium membership of the OOTLE. The Foreign Secretary is the second-most popular politician in Britain, overtaken only, when she became Prime Minister, by Theresa May herself.

If there is one person who won the referendum on leaving the EU, it was he. There wasn’t one person, of course; Michael Gove, who declared for Leave first, helped to pave the way for him. Jeremy Corbyn was quite important, in the negative sense of failing to mobilise the Labour vote for the Remain cause. Even Douglas Carswell, the Conservative defector to Ukip who helped to sabotage his new party and to keep Nigel Farage out of the official Vote Leave campaign, played a part.

But Johnson was the most powerful actor on the Brexit stage. And like many actors he has a clownish side, but to dismiss him simply as a joke would be to misread politics and to misunderstand one of the central puzzles of the May Government.

That puzzle is the background to Johnson’s uncertain handling of the Syria crisis.

Inevitably, the true story is more complicated than the caricature of Boris as Donald Trump’s blunderingly incompetent poodle, which was the media consensus over the weekend. When the Foreign Secretary cancels a trip to Moscow the day before he was due to fly, as Johnson did on Saturday, it was clear that something was not right. But it was unclear whether it was the US, Number 10 or Johnson himself who was most important in the decision to cancel. In fact, it was sensible to stay away: there was a risk that the Russian government would try to play Johnson off against the Americans or to humiliate him.

But Johnson does seem to have misjudged today’s meeting of G7 foreign ministers, having talked up sanctions against the Syrian regime and the Russians yesterday only for the others to back off from “pushing Russia into a corner” in the words of Angelino Alfano, the Italian foreign minister. Which is awkward, given the reports of a split between Johnson and May that surfaced in The Sun yesterday – he was said to be more hawkish about supporting future US strikes against Syria than the Prime Minister.

I will leave others to pronounce on who is right, and to try to interpret whether the policy of the UK Government – or of the Trump administration – is to tolerate Bashar al-Assad, preferably without chemical weapons, or to replace him, and, if so, with whom. What may be more important for British politics is what it means for the relationship between May and her Foreign Secretary.

The main point of Johnson, to return to the Brexit referendum, is that he wanted to be prime minister, and that May’s appointment of him to one of the great offices of state meant that his ambition might have been deferred rather than denied. She certainly seems to regard him as a rival for her job who must be contained. He was not allowed to bring Will Walden, his adviser and spokesperson, with him when he joined the Government. She made him the butt of her jokes, asking the Tory party conference last year: “Can Boris Johnson stay on message for a full four days?” And the teams around May and Johnson seem to get on badly; journalists are often told different things by the two camps.

This does not feel like a story that is going to end well. Johnson has been unsackable for the past nine months, as the most important member of the Brexit ring of steel around the PM in the Cabinet. Now that May has invoked Article 50, however, she does not need her human shield so much, although it would still be damaging to her to lose him. Here she is in a catch-22 familiar to prime ministers through the ages: she needs him because he is popular, but then he is a threat; he would be less of a threat if he became less popular, but if he did that by doing the job badly it would hurt her Government too.

It is possible, however, that the Prime Minister is mistaken if she feels that he is a threat to her position. In the days after the referendum Johnson, on the cusp of seizing the premiership, seemed to have had a crisis of confidence in himself. It was not just that Gove betrayed him, damaging as that was, but that his hesitation and indecision helped push Gove into treachery.