The presidential administration is the most powerful institution in Vladimir Putin’s deeply personalised system: it feeds him the intelligence he wants, it oversees ministries and governors, and it coordinates his “active measures” political dirty tricks campaign in the west. This spring, I sat down in Moscow with an astute former staffer of the presidential administration and he remarked that Putin demanded apparent success today at the expense of real success tomorrow. Brexit may prove the perfect case study.

This should not be a great surprise. To portray Putin as the masterful geopolitical chess-player has become a familiar cliche. But in recent years, Putin seems to have become increasingly insulated from bad news and critical opinions, and has made serious mistakes as a result. In particular, he and his cronies time and again have shown themselves unable to understand democratic societies, and the resilience that lies beneath the surface of fractiousness and short-termism.

If Putin ever deluded himself that his campaign of hacks, disinformation, covert political donations and other gambits was going to allow him to shape the western political agenda, he ought now to be having second thoughts. Admittedly Russian meddling has managed to worsen existing political and social tensions throughout the west, from playing to an Islamophobic nativism in Europe, to the populist resentments that fuelled the Trump campaign.

Yet to what real advantage? Nato has regained its focus on the challenge from the east and is now spending more on defence. Key European leaders such as Emmanuel Macron and Angela Merkel are unequivocal about Moscow being a dangerous influence. Investigations, rumours and court cases are boxing in Donald Trump. Even the Brexit vote, which undoubtedly delighted a Kremlin eager to see Europe divided and discordant, now looks open to question.

All told, it would be a fitting irony if, of all people, it was Putin who saved Britain from Brexit. A steady trickle of hard information and soft rumour about Russian support for Brexit risks becoming a torrent. Some of this support was, frankly, of questionable impact. Too much is often made of the alleged influence of the English-language Sputnik news agency and RT television channel, or even of the online trolling and disinformation campaign. Evidence that they actually changed minds – rather than just pandered to existing prejudices – is still lacking.

However, there is a growing likelihood that later this year or early next we will see solid evidence of financial support for the Brexit camp, too. MP Ben Bradshaw has used parliamentary privilege to raise the question of the mysteriously bottomless pockets of Arron Banks, the main backer for Leave.EU. The Electoral Commission this week launched an investigation into whether he and one of his companies broke campaign finance rules in the run-up to the referendum. George Cottrell, once an aide to the former Ukip leader Nigel Farage, has been arrested by the FBI on money laundering charges, and we await the outcome of that investigation.

Meanwhile, according to US intelligence sources with whom I have discussed Moscow’s activities, there are other cases of what the Russian spooks call “black cash” supporting pro-Brexit campaigns and campaigners, likely to be revealed over the course of the several inquiries taking place on the other side of the Atlantic. Of course, assessing the impact of these operations will require careful study and scholarly rigour. But when has this stopped anyone using eye-catching allegations for political advantage?

Ironically enough, this may come at exactly the right time to let a British political elite increasingly alarmed about Brexit off the hook. There is public dismay at the slow progress of talks, but no clear mandate to reverse policy. Hard evidence of active, covert Russian interference would delegitimise the original vote, given the narrow margin of victory. Hardcore Brexiteers will risk looking like Putin’s “useful idiots”.

This would allow the government to re-run or even disregard the referendum without looking as if it is admitting a mistake or challenging the popular will. It would also smooth the way to allowing article 50 to be revoked or ignored with no penalty. (While the EU is formally committed to allowing the UK to change its mind, there are those in Brussels with more punitive intent.)

Putin’s self-harming passion for subversion seems to be the toxic product of a KGB background, a nationalist’s anger at the decline of the superpower and a lack of other, more acceptable, ways of advancing Russia’s agenda. As Putin pushes his spies, trolls, diplomats and lobbyists to take every opportunity to divide, distract and disrupt the west, whatever the long-term cost, he risks making his country into a pariah state.

It is possible that his active measures helped tip the balance in the Brexit referendum. Even more likely, they will help tip the balance back.

• Dr Mark Galeotti is a senior researcher at the Institute of International Relations Prague and head of its Centre for European Security