Garvan Walshe is a former National and International Policy Adivser for the Conservative Party. He runs Brexit Analytics.

The local newspaper in the West Cork town of Skibbereen was once called the Eagle. Mesmerised by the Tsarist threat, it bore on its masthead the slogan “Keeping our eye on Russia.” That is no more but its role appears to have been taken up by the Mail on Sunday, determined as it is to find reds under the bed at a townhouse at Number 11, Charles Street, Mayfair.

The Remainer circles from which this column sometimes serves as emissary are buzzing with excitement. Could it be that Brexit is not in fact the culmination of 40 years of campaigning by Brits hostile to membership of the EU, but instead a dastardly Russian plot? The most committed McCarthy revivalists even point to the fact that the investment fund run by the Chandlers, the family behind the Legatum Institute, and Dominic Cummings, appear to have been in Russia at the same time. They will be disappointed when they find out that Russia is – how shall I put this? – a big place.

Moscow benefits not only from its size (17 million square kilometres, according to Siri), but also from an outsized reputation for intelligence wizardry, sedulously cultivated by Graham Greene and Ian Fleming, and blessed with a leader who was once a colonel in the KGB.

There’s no doubt that Putin’s Russia has malevolent intent. With an economy the only slightly larger than Spain’s ($1.3 trillion, to Spain’s $1.2 trillion, at current prices) Moscow styles itself a world power: sending troops to Syria, wielding its veto on the UN Security Council, maintaining a huge nuclear arsenal and invading its neighbours. But a revived Soviet Union it is not: it is more like a puffer fish, poisonous if you swallow it, but much smaller than it looks.

Its stroke of luck was to discover the potency of emotional and divisive political communication on social media, which it used to great effect in Eastern Europe before the EU referendum or Trump election campaign were ever thought of.

It is certainly possible that Russian efforts (paid for in Roubles, with startling naivité) just got Trump over the line, so close was his technical win in Wisconsin (27,000 votes) and Michigan (11,000 votes). And Moscow hit the short term jackpot: a US president on whom it seems increasingly likely they have compromising material, who appointed as National Security Adviser a man on a pro-Russian Ukrainian oligarch’s payroll, and whose campaign team, instead of reporting Russian attempts to meddle with the American election to the FBI, took steps to benefit from them. And the intervention in elections succeeded beyond all expectations in that it has robbed the United States of its soft power, undermined its credibility in the Middle East, and enabled the appointment to the State Department of a man determined to encourage the most capable and experienced of American diplomats into retirement.

If Russia might well have got Trump over the line, helped by a much larger quantity of indigenous American fake news, the idea that the Kremlin managed to do the same with the Leave campaign does not stand up to scrutiny. Compared to the weight of the British- (or Australian-) owned pro-Brexit press, and the nonsense put out by the Leave campaign (£350 million savings which ignored the rebate; claims that Turkey would join the EU and that an EU army would be created, both of which the UK could have vetoed had it stayed in) and a well-developed and entirely sincere, decades old, pro-Brexit campaign, any Kremlin effect is a rounding error.

Of all the claims made, perhaps the most plausible is the allegation levelled in some quarters that the undisclosed donation to the DUP by the Constitutional Research Council might actually have been from Russia – though that is still unproven. Even if it turns out to have been, the reality is that neither side was short of money. And insofar as there may have been alleged Russian influence on Leave.EU, that campaign’s function was different: to normalise a more extreme position. Here, Leave had a lucky escape: had Leave.EU been designated the main Leave campaign, the pro-Brexit side would never have attracted senior Cabinet ministers or the credibility needed to win.

Even if Moscow did manage to nudge the dial a little, it could get more than it bargained for. By helping to remove the main obstacle to European military integration, any Russian campaign for British withdrawal may have effects that far exceed the $7 billion reduction in the British defence budget attributable to the weaker pound.