There are many gripping moments in McMafia, the BBC’s lavish new television drama featuring Russian oligarchs and organised crime. Who knew that a caviar knife could be so deadly? Or that hired killers could run amok in the Home Counties, leaving a bloody message from Moscow all over the tasteful furnishings?

For Russia purists, there are a few quibbles. Would Alex Godman – the British-educated son of a Russian gangster, played by James Norton – really talk to Dad in accent-free English? And where exactly are the bodyguards? They are an obligatory feature of life for any self-respecting Moscow businessman but strangely missing here when their tough-guy skills might come in handy. But the ideas underlying McMafia – taken from the nonfiction book by the journalist Misha Glenny – are surely right. International crime syndicates are able to shift huge sums of money around the world, still. This is thanks to a financial and banking system that allows them to hide behind anonymous company structures, and asks few questions.

Investigative journalists have been busy peeling back these layers of offshore secrecy. In 2016, the Guardian and media partners published the Panama Papers, based on records from the offshore law firm Mossack Fonseca. Mossack specialised in setting up opaque shell companies. As Bastian Obermayer, the German reporter who got the leaked data, put it, its clients were frequently “scumbags”. We found drug dealers who might have sprung from McMafia. And arms smugglers, oligarchs, defence contractors, gambling fraudsters and kleptocrats. Plus politicians, sports stars and prime ministers. Vladimir Putin’s old friend – a St Petersburg cellist called Sergei Roldugin – was linked to the flow of billions of dollars from offshore accounts. The cash went from Russia, to Panama, the British Virgin Islands, and back to Russia again.

In one telling scene from Monday’s opening McMafia episode, Alex Godman discusses how he might magic funds to Mumbai “without leaving a trace”. His answer: by setting up an elaborate chain of companies in different tax havens. A “special purpose vehicle” in the Caymans would lend money to another similar vehicle in the Bahamas. And so on. This is classic money laundering. It may sound like fiction. Depressingly enough, it’s real.

Not everyone who uses offshore vehicles is a crook. But the main takeaway from the Panama and the Paradise Papers, published again by the Guardian and media partners in November, is that the offshore industry is not a minor, shadowy part of our economic system: it is the system. The burden of taxation has moved away from multinational corporations and the rich to ordinary people. Offshore has made this happen. We – those of us who pay our taxes – are the dupes.

Glenny is right about something else: the central role of the UK, and London, in facilitating the flow of money. We flatter ourselves by thinking that this takes place somewhere far away. Much of it happens on our doorstep, among the manicured terraces of Belgravia and Kensington, where much of McMafia is lusciously shot. British law firms, estate agents and company formation agents are the chief enablers.

Take one micro-example. The London solicitors’ firm of Child & Child looks respectable enough: an office overlooking Buckingham Palace gardens, a website featuring neoclassical Georgian mansions and a lot of fluted columns. In 2015, Child & Child set up a secretive offshore company in the British Virgin Islands, a leading UK tax haven. The firm’s beneficiaries were Leyla and Arzu Aliyeva, the daughters of the president of Azerbaijan.

Like children from other ruling post-Soviet dynasties, the Aliyevas own extensive property in London, worth many millions of pounds. The new offshore company, Exaltation Ltd, was set up to hold their real estate assets. Child & Child was supposed to identify the Aliyevas as “politically exposed” individuals. This would have triggered extra banking checks into the family’s wealth. It didn’t. Nothing happened to the firm. It wouldn’t comment.

Meanwhile, international money launderers have a distinct preference for the kind of companies they like to use: UK ones, with posh-sounding names. Between 2010 and 2014, Russian insiders moved at least $20bn of dirty money from Moscow into the western financial system. The scheme was ingenious. It involved Moldovan judges, a Latvian bank and a series of hub-companies, incorporated at Companies House in London. These were “managed” by firms sitting in remote tax havens.

Before writing our first report on this, I posted letters to the Marshall Islands, a sunny atoll nation in the Pacific. I never received a reply. This wasn’t a surprise: these “managers” were brass-plate entities, with no meaningful existence. (I could, I reflected, have put my right to reply letters in a bottle and chucked them into the sea.) The UK National Crime Agency expressed interest in our findings but said there was little it could do. The perpetrators were far away. It was all a bit difficult.

Theresa May’s government has shown no interest in taking modest reforms further

Banks too shrugged their shoulders. High-street banks and foreign subsidiaries with offices in London processed $738m in transactions from what was called the Global Laundromat. All of them had sophisticated units dedicated to rooting out financial crime. The problem was volume: billions worth of payments each day. “If you are on the back end, you are kind of playing whack-a-mole trying to pick this up,” one bank source told me.

What then can be done about the McMafia culture, thrillingly brought to life on our TV screens, and doubtless featuring more violence and gore in the episodes to come? In May 2016, David Cameron promised a new public register that would for the first time identify the “significant” person behind a UK company. It was a start. Two months later Cameron exited as prime minister.

Theresa May’s government has shown no interest in taking these modest reforms further. One measure would be a game-changer: for the UK to compel its overseas territories to bring in similar public registers, which would disclose who owned what. More than half of all companies from the Panama Papers were set up in the British Virgin Islands.

True, Russian oligarchs like McMafia’s Dimitri Godman might get round this by using nephews, friends or chauffeurs as proxies. Or by simply lying. Nevertheless, the reform would bring new transparency. It would curtail the culture of anonymous ownership that has blighted London’s property market. It might show that the UK is serious about tackling organised crime. The consequences of McMafia are all around us: a divided society, and a capital that has become a playground for the internationally dodgy. They steal at home and enjoy legal protections here.

• Luke Harding is a former Guardian Moscow correspondent, and author of Mafia State and Collusion