Earlier this week Donald Trump stood on the south lawn of the White House and ridiculed Theresa May’s Brexit agreement as a “great deal for the EU”. He is likely to make the same contemptuous case during the G20 summit in Argentina this weekend, although pointedly there is no planned bilateral. Given the political stakes facing her back home, Mrs May must feel as if 14,000 miles is a long way to travel for the weekend merely to be trashed by supposedly her greatest ally.

When this happens, though, who does Mrs May imagine is confronting her? Is it just Mr Trump himself, America First president, sworn enemy of the international order in general and the European Union in particular? That’s a bad enough reality. But might her accuser also be, at some level, Vladimir Putin, a leader whose interest in weakening the EU and breaking Britain from it as damagingly as possible outdoes even that of Mr Trump? That prospect is even worse.

Such speculation would normally seem, and still probably is, a step too far. The idea that a US president is in any way doing the Kremlin’s business as well as his own is the stuff of spy thrillers and of John le Carré TV adaptations. Yet the icy fact is that the conspiracy theory may now also contain an element of truth.

On Thursday, Mr Trump’s longtime lawyer, Michael Cohen, pleaded guilty – in a court filing by the special counsel Robert Mueller – to lying to the US congress about Mr Trump’s Russian interests and connections during the months when the New York property magnate was running for the Republican presidential nomination in 2016. It was not true, Mr Cohen has now admitted, that the Trump organisation ended its interest in Russian deals in January 2016; not true that there were no plans for Russian visits by Mr Trump later in 2016 to make property deals; not true that the Russian government did not respond to the deal overtures. Indeed, as late as May 2016, Mr Cohen was in indirect contact with Mr Putin’s office about the possibility of a meeting with Mr Trump in St Petersburg in June.

Days before he took office in 2017, Mr Trump said that “the closest I came to Russia” was in selling a Florida property to a Russian oligarch in 2008. If Mr Cohen’s statement is true, Mr Trump was telling his country a lie. What is more, the Russians knew it. Potentially, that raises issues of US national security. If Mr Putin knew that Mr Trump was concealing information about his Russian business interests, this could give Moscow leverage over the US leader. Mr Trump might feel constrained to praise Mr Putin or to avoid conflicts with Russia over policy.

All this may indeed be very far-fetched. Yet Russia’s activities in the 2016 election against Hillary Clinton and in favour of Mr Trump are not fiction. They prompted the setting up of the Mueller inquiry into links between the Russian government and the Trump campaign. Another document this week suggests a longtime Trump adviser, Roger Stone, may have sought information about WikiLeaks plans to release hacked Democratic party emails in 2016.

There is nothing in the documents released this week that proves that Mr Trump conspired with Russian efforts to win him the presidency. Yet those efforts were real. For two years, Mr Trump has gone to unprecedented lengths to attack the special counsel. After November’s midterms, he seemed on the verge of firing Mr Mueller. He may yet do so. But this week’s charges suggest that there is plenty more still to be revealed. Mr Trump still has questions to answer from the investigating authorities, from the new Congress – and from America’s long-suffering allies.