Elements of the 2016 British referendum campaign have long seemed familiar to Americans. There was a close, controversial election, full of rancour and anger. There were a lot of wealthy men talking about “the people” and their “will”. There were targeted advertising campaigns, stolen data and fake social-media accounts.

But now, with only a few days left until Britain is due to face the consequences of that vote, the Brexit story suddenly looks even more familiar: one of its protagonists turns out to have much deeper Russian business connections than previously suspected. He also tried to conceal them.

The protagonist in question is Arron Banks, the most important funder of both the pro-Brexit UK Independence Party and Leave. EU, one of several organisations that campaigned to get Britain out of the European Union.

By the relatively low-spending standards of British politics, Banks was a huge donor, giving $11 million of his own money to the Brexit cause and raising an additional $5 million on top. And here’s the peculiarly British part of the story: thanks to Banks’s extensive use of tax havens and shell companies, it has never been entirely clear where all of that money came from — or even whether all of it was really his.

Some of it, he says, comes from an insurance company he owns. Some comes, supposedly, from “diamond mines”. All of it is spread among dozens of companies based in Gibraltar, the British Virgin Islands and the Isle of Man, according to documents revealed in the Panama Papers, among other things, as well as Britain.

Although he has testified that none of the money used in funding the campaign came from foreign sources, which would be illegal, the British electoral commission found his stories suspicious enough to ask the National Crime Agency to investigate.

Banks also seems to have been very friendly with some foreigners who also believed that Brexit was in their national interest. Last summer, The Guardian reported that the Russian ambassador to Britain had offered him a tantalising and peculiarly lucrative investment in Russian goldmines; Banks declared categorically that he would never invest in Russia: “No. Flat. Zero. Nothing,” he replied when asked directly by Channel 4 News.

This past week the broadcaster’s reporters alleged that a finance company substantially owned by Banks did pursue the deal — and even identified a shell company, based in Sweden, that could be used to pursue it. Because Banks still denies that the deal happened, and because the story is so hard to follow further, we will not know the truth before March 29, when Britain is scheduled to leave the EU.

But even if this story will not delay Brexit, it does firmly locate the referendum within a larger context. The truth is that Britain has become a place where untransparent money, from unknown sources, is widely accepted with a complacent shrug.

London is the world capital of offshore banking, home to the most sophisticated accountants and lawyers; one third of British billionaires has taken advantage of those services and moved money beyond the reach of the state, according to a report last Thursday in The Times. Many of them nevertheless continue to make donations to British political parties, and many continue to lobby to keep the rules that favour them exactly as they are.

As a result, the British political class does not have the willpower to force them to bring their money home. The British state does not have the legal tools to force Banks to show where his cash came from. The British media continue to investigate, but if anyone were trying to influence the British referendum campaign from outside the country — beyond the social-media manipulation that is now de rigueur in almost every election — it is possible that we will never know.

And here’s the final irony: if Brexit was the creation, in part, of this new world of offshore money and political influence campaigns, Brexit may well ensure that it continues unrestricted. The EU is probably the only power in Europe — maybe even the only one in the world — with the regulatory strength to change the culture of tax avoidance. And since 2016, it has been slowly enacting rules designed to do exactly that.

Britain, once it leaves the EU, may well be exempt.

British industry may suffer after Brexit, and British power will be reduced. But the grey zone — where politics meets money, where foreign money can become domestic, where assets can be hidden and connections concealed — will survive. Perhaps that was the point all along.

• Anne Applebaum is a Washington Post columnist, covering national politics and foreign policy, with a special focus on Europe and Russia. She is also a Pulitzer Prize-winning historian and a professor of practice at the London School of Economics. She is a former member of The Washington Post’s editorial board