‘Data rights are human rights” is the rallying cry of this gripping, challenging documentary by Karim Amer and Jehane Noujaim, about the biggest scandal of our time: the gigantic question mark over the legality of the Brexit vote.

It is about the Trump campaign, the Leave.EU campaign and many other reckless electoral adventures all over the world and their connection with Cambridge Analytica, the British data research company that cunningly harvested information from millions of Facebook users and their friends via an innocuous-seeming “personality” questionnaire. They put this gigantic database to lucrative work with machine-tooled marketing campaigns for Trump and the Brexiters; after the company declared bankruptcy, its documentation may never come to light.

At the centre of the film is Brittany Kaiser, a former Cambridge Analytica employee who blows the whistle on her employers’ connections, including those with the Bad Boys of Brexit, whose bad-tempered éminence grise Arron Banks is now trying to silence Observer journalist Carole Cadwalladr – as well as this film – with legal threats.

We are aware of these issues in the first place only because of the magnificently tough investigative reporting by Cadwalladr, who asks if we can ever again have a free and fair election. She has had to face down bullying and supercilious condescension from many quarters. The Great Hack is also about the US media academic David Carroll who launched a legal campaign in the UK to force Cambridge Analytica to reveal their “data report” on him. I was reminded of historian Timothy Garton Ash’s efforts to find his Stasi file, written by spies in the former East Germany. Ash was successful, but Carroll will probably never see his data digital dossier.

There is evidence pointing to campaign finance laws being broken. Yet perhaps the larger point is that these were framed in the quaint era of printed posters and ads in newspapers, and analogue television. These laws are not fit for purpose. The data weaponisers are laughing at them, and us.

Trump and Brexit won on a knife edge and Cambridge Analytica’s triumph was to identify the wobblers, the undecideds, the could-go-either-way-ers in the middle: the “persuadables”. This narrow band of voter opinion in the centre is all-important, like the “tipping point” Malcolm Gladwell identified as the key moment in a viral phenomenon, or that stage in a game of blackjack that card-counters recognise is their moment to bet 10 times their usual stake and beat the house.

The data attackers could go all in, using their underhand knowledge to bombard these psycho-profiled targets, to push these persuadables’ buttons and tip them over the edge with Facebook ads that popped up intimately on their smartphones, miraculously confirming their prejudices, playing on their insecurities, magnifying and warping their worries: people who didn’t realise that their private data-identity had been sold to people who as a result could now personally solicit them without their knowing.

Perhaps the most chilling part of the film shows that a Cambridge Analytica operative worked on a campaign in Trinidad and Tobago in 2013, inciting a certain strand of the population – assessed as liable to support the clients’ opponents – not to vote, creating a bogus grassroots anti-establishment campaign with the ironic slogan “Do So!” The point of course was not to “do so” or do anything at all, not to vote, in fact: an insidious argument for apathy. Anyone who says voting is a waste of time needs to watch this film, if only for this segment.

The Great Hack repeatedly plays a recording of Cambridge Analytica execs giggling about their role in the Brexit campaign, a role they had wanted to deny: “Oops, we won!” Oops indeed. However gung-ho they were about foreign clients, the good boys of Cambridge Analytica were clearly a bit sheepish about the triumph closer to home and, like besuited Westminster Brexiters such as Boris Johnson, imagined simply an exciting bit of risk-free disruption to boost their brand. What they helped bring about was dishonesty, cynicism and chaos.

• Released in the UK and on Netflix from 24 July.