That characterisation is imprecise to the point of being misleading; may I tell the story in detail?
I particularly rebut any suggestion that the Tories organised the referendum. That's only true at the most superficial reading. The whole farrago (pun intended) was founded by fringe nutters in the party, offered as a sop by the party leadership, and co-opted and orchestrated by interests inimical to the nation. (There is a case to answer for treason.)
Ever since the first referendum to join the EU in 1975, the anti-Europe faction of the Tory party was muttering in dark corners.
They gathered political strength at the fringe, slowly bolstered by drips of propaganda such as Boris Johnson's baseless claim, as a journalist, that the EU regulated the bendiness of bananas. In 2013, a nameless senior Tory in the orthodoxy coined the phrase "swivel-eyed loons".
Boris Johnson, may he swing, is every bit as much a fabricator as Donald Trump. If truth enters his speech, it's because it got lost.
_Aside: English politics has always been a straight left-right axis, with the left split between Labour and Lib Dems but the right united in the Tories. Labour had always had a strong socially-conservative constituency, but social conservatism has never been a campaign theme, AFAICR, beyond "tough on crime", which is a cheap vote-winner for anyone anywhere. The Labour Party is relatively new, but the Tories and Lib Dems trace their ancestry back to the same Tory-Whig axis that America inherited. Brexit turned that axis into a quadrant, with the LDs united but with the Tories and Labour split._
After they dicked over the plebs with austerity in a recession, the nation was angry with neoliberals, and the anti-EU gang fed on that. Not without reason, given how Greece got the shaft to protect German investors.
Campaigning for an outright majority in 2013, Cameron (a widely-used nickname for Pigfucker) offered the loons a referendum to keep them inside the tent; if the right split, it would have been a huge embarrassment for him. At that point, an anti-EU platform would not have taken many votes, but they would mostly have been Tory votes.
The Tories were already a neoliberal govenment, and they were blithely confident that they would win the referendum - it was a free hit for the loons, which was supposed to shut them up for another decade. Cameron had nothing to gain except silencing an annoying sideshow. He was already five years into an aggressive neoliberal strategy.
He shrugged off the power of bullshit stories such as "bendy bananas" and "Romanian squatters", despite the fact that they were in the Sun (proles), the Mail (proles with pretensions of intelligence), the Spectator (unintelligent toffs), and the Telegraph (obedient middle class). My apologies if you take the Spectator for the cartoons.
Despite their swivelly eyes, the Leave campaign acquired a huge war chest - namely, money from forex speculators and from Russia, which tells you exactly who benefits.
_Aside: London has been a haven for Russian money since glasnost. Russian oligarchs had been funding the Tories for years. Russia had total access to English politics up until the 2022 sanctions. The report from the inquiry into Leave campaign irregularities was suppressed._
The Leave backers brought in Steve Bannon, fresh from Trump's campaign. Bannon is not a great talent, but, in the milieu of English political campaigns, he was ahead of the curve. England was unprepared for bare-faced lies being astroturfed on Facebook.
Meanwhile, Cameron burned his war chest on fucking leaflet drops.
Cameron failed to generate any positive talking points, and expected to win by default. He argued that we'd become poor if we left Europe, which did little to sway working-class voters whom he had spent 6 years impoverishing. This arrogance was reflected by Gove's soundbite "people in this country have had enough of experts".
A new constituency emerged: "gammon", named for their ruddy complexions; choleric boomers, typically educated and middle-class but who long ago waved goodbye to curious intelligence, susceptible to and active on Facebook. These people are not as bad as your American fox news zombies, but of the same ilk - spittle-flecked rants at the breakfast table, "simple common sense", highly emotional yet sublimely certain of their own rationality. These chumps did not have a legitimate grievance against the government or the EU; their apoplexy was inchoate; they were merely channeled by the grifters.
Combine the gammon with the uninformed working class plebs, who bought into the threats of waves of gypsies arriving from Romania and mixed it with baseline sentiment against immigrants from all countries, and also the huge constituency that just wanted to give the arrogant neoliberals a black eye, and you have a win against the odds for Leave.
Excuse my rambling. It's hard to be concise when you're incandescent with fury.