“Just got through reading the Lisbon treaty! OMG!!!” and “Why is no one talking about the Lisbon treaty that comes into force in 2020???” Suddenly it’s viral. If you see this everywhere online you may puzzle how the treaty’s 3,000 dense pages have become such hot reading across Facebook, Twitter and Reddit. Look, for example, at what one (now deleted) tweet claims of what staying in the EU means: “Just been reading some of the Lisbon treaty, very worrying. By 2020 we lose our veto, control over fishing, agriculture and more. Also by 2022 all countries must adopt the euro. How can Theresa May and our MPs want to keep us in such an appalling club?”

This new wave of fakery about the Lisbon treaty is a useful warning about what the remain cause faces

Post after post is spreading a fake list of the treaty’s contents. If Britain stays in the EU, by 2020 we will be locked into vassalage of a new super-state. There is never, of course, any quote or link to the real treaty. So who’s doing this? Are these posts real, Russian, or US-financed far-right bots, generated by any of the linked Brexit groups under different names? Impossible to tell, says Steve Peers, a professor of EU law at Essex University who has been chasing down this monster with painstaking rebuttals, refuting it point by point. He says the similarity of the words used – the “I’ve just been reading the Lisbon treaty” phrasing – suggests a highly organised and well-financed campaign of disinformation, backed by expensive ads disseminated virally.

If it weren’t so avidly believed and shared, this absurdity could be ignored, but it’s typical Brexitology. Here are its claims: in 2020 all EU countries lose their veto. In 2022 all become states of the new federal nation and must join the euro. The London Stock Exchange will move to Frankfurt to an EU exchange and the EU parliament and court of justice become “supreme”. Borders are lost as Schengen becomes compulsory and countries lose control of planning and tax policies. The UK hands over its armed forces and nuclear deterrent to an EU force.

There’s a lot more of this balderdash, with each claim meticulously debunked by Peers. No, nothing new is about to be enforced: there is no mention of 2020 or 2022 in the real treaty, as all was fixed in 2009. No, the word “federal” is not in there, except in Germany’s official name. No, the veto isn’t being lost, while the need for unanimous votes gets 100 mentions. Some claims sound vaguely plausible: true, we have no absolute control of our fisheries and never did, in or out of the EU. But no, the UK won’t lose the Falklands, Caymans and Gibraltar.

This new wave of fakery has been sparked by Brexiter fears that Britain may not leave after all – or that Labour’s (semi) support for a confirmatory referendum will mean another vote. If so, this is a useful warning of the kind of submarine disinformation the remain cause faces, the ocean of fake facts that never surface into the light of day where they can be refuted publicly. This poisoning of the political bloodstream is hard to counter. Remainers’ weakness is their innocence: they would never fight this dirty. But why is Britain vulnerable to such conspiracy rubbish? Those with the least education are most prone to believe conspiracy theories such as these anti-Europe tropes – and the least educated group are older generations. Britain being undone by its longstanding failure to give a good education to all, cherry-picking the grammar school few for so long, is apt revenge for decades of neglect.

‘No prime minister since Edward Heath has celebrated the benefits of Europe.’ Photograph: Stefan Rousseau/AP

Blame our leaders too. No prime minister since Edward Heath has celebrated the benefits of Europe. All have bowed to anti-European populism, striding to EU summits as if to war, boasting of red lines, bragging of bogus “victories”, never welcoming mutually beneficial pacts. Margaret Thatcher began it, but even Tony Blair, now such an eloquent European advocate, failed as prime minister to make a single speech in Britain on the EU, let alone one in praise. Gordon Brown, now an equally ardent anti-Brexiter, skulked off to sign the Lisbon treaty out of sight of cameras. Just look what David Cameron did next. Yes, the EU certainly needs radical reform, but British voters have only ever heard negatives. So now we reap the whirlwind of disinformation spread by every prime minister too afraid of a bullying Europhobic press to praise the peace, prosperity and global influence Britain has gained inside the world’s greatest democratic alliance.

But we are where we are, with too many people prone to believing dangerous lies. Weeks away from the Brexit deadline, the prime minister may manage to frighten enough of her MPs into backing her deal, with threats of no deal or no Brexit. But her cheapskate attempt at bribing some 30 Labour MPs into her camp should send them howling in rage back to their own side.

Her £1.6bn for all coastal towns, all the north and Midlands, thinly spread over seven years, is an austerity insult. Compare that with the £4.2bn the Treasury is spending on Brexit preparations. Compute what these areas have lost: their councils cut by more than 40%, schools impoverished, people stripped of billions in benefits. For the north-east that’s £40 per head – over the seven years. What MP will be bought so cheap?

Labour MPs who enable May’s Brexit should be warned. If she gets her deal over the line, the momentary national sigh of relief will last only a nano-second. If they foolishly imagine they can later win some gentle Norway option during the transition, they forget the Tories will replace May with a hard-Brexit leader bent on a minimalist, Canada-style deal. Labour MPs who vote for her deal, clueless and powerless over its true destination, will be for ever blamed for the consequences. Better by far to let the voters decide, and tackle the tide of disinformation head on.

• Polly Toynbee is a Guardian columnist