It's hardly a surprise that Russian and American views of the world differ sharply. But there is one area of unexpected congruence in Moscow and Washington: Brexit. Travelling between both capitals, it is hard to tell the difference between the perplexity and even suspicion with which Britain's ongoing and bungled departure from the EU is being viewed.

Of course, the two administrations have rather different interests when it comes to Brexit. In the United States, there is some excitement among big business about the prospect of the UK market opening up. In the main though the feeling is one of dismay about the crisis gripping one of the country's closest allies. US national security adviser John Bolton may present Donald Trump as “eager for the will of the British people to be carried out”, but in Washington last week I heard sober State Department folk worry that, in the words of one, “America might find itself gaining an economic client at the cost of a geopolitical ally.” It is not that they felt a post-Brexit UK would be any less of a friend, just that it would be a much less useful one.

Conversely, Brexit is an unexpected boon for a Kremlin actively seeking to sow division and discord in the West. Foreign minister Sergei Lavrov may have denied that Russia was “rubbing its hands and gloating”, but he was being disingenuous. Vladimir Putin himself has weighed in on the subject, complaining that “Brexit happened, but no-one wants to implement it.” (Indeed, breksit’ has even become a word in Russian for claiming that one is about to leave a party or the like and yet never actually heading out the door.) One person I spoke to in Moscow, tongue wickedly in cheek, suggested to me that David Cameron ought to be in line for the Order of Alexander Nevsky, awarded for particular services to Russia’s interests abroad.

Yet the irony is that however far apart Moscow and Washington may be geopolitically, there is a striking similarity in how they perceive – or maybe perceived – the UK. The challenge of understanding Brexit from a distance (it’s hard enough at close range, after all), both reflects and tests traditional perceptions of the Brits. Central to this are long-held assumptions about British political stability and managerial competence. Whatever else, the notion was that the Brits knew how to get things done, especially when it came to brokering consensus and negotiating complex undertakings.

Then came Brexit. As one veteran Russian observer put it to me, “I wasn’t surprised the British decided to leave the EU. I was surprised they didn’t seem to know quite how. I’ve been amazed that three years later, they still seem to have learned nothing.”

There is a shared perception that the British mask a sneaky soul behind their forthright image though, and it is interesting how far, in both countries, this led to off-the-record suggestions, perhaps best characterised as wistful hopes, that things could not truly be as chaotic as they seem. Saying that “these are not the Brits we thought we knew,” one American official wondered whether “it is just that we are not seeing the full picture.”

After all (or so the logic goes) in Britain, public discourse does not fully reflect behind-the-scenes politics, shaped as they are by indefinable, almost inexplicable shared assumptions; the “private code of the private school elite” in the words of one American. The Russians even use the word ponyatiya, ‘understandings,’ an amorphous term as often encountered when talking about gangsters as politicians.

As a result, at least some of those I met in both the United States and Russia felt that surely – surely – there must be some subtle and secret designs behind the apparent deadlock and drama. The favoured scenario amongst these conspiratorial optimists was that this was, in the Russian term, dramaturgia, a carefully-choreographed spectacle of apparent haplessness and impending chaos intended as eleventh-hour and fifty-ninth-minute gamesmanship with Brussels. To those Americans, this was clearly a desperate hope; to the Russians, a reflection of their age-old belief that perfidious Albion is the most cunning and ruthless rival they face.

It felt unfair to burst their bubbles of respective optimism and suspicion, though maybe I am just being naïve in my assumption that what we see is what we are going to get. But I somehow doubt it.

In any case, it does seem clear that one of Britain’s intangible assets, its reputation as a country that manages somehow to combine robust good sense and clinical pragmatism, survives – so far. Of course, one could argue that this image shouldn’t have endured as long as it did, but in Washington and Moscow my own experience is that repute can outlast the end of empire and ruling class alike, in antagonist states as well as allies. But it may not outlast Brexit.

Mark Galeotti is the author of We Need to Talk About Putin: Why the West Gets Him Wrong, and how to Get Him Right