A turbocharged version of the Transatlantic Trade and Investment Partnership (TTIP) could be heading Britain’s way after Theresa May’s Brexit white paper. That’s the upsetting irony for those (and there were a few) who voted to leave the European Union to escape nasty trade deals that involve secret courts to resolve corporate disputes.

These are the courts that some of the world’s biggest companies have used when they want to overturn local laws that jeopardise their profits. Tobacco company Philip Morris was a keen exponent. Its legal suits in Australia, Uruguay and others against plain cigarette packaging caused an outcry and cost the respective governments millions of pounds in legal fees, even though it failed.

It is a racing certainty that secret courts will be part of any trade deal with the US because even the Obama administration insisted on them. The infamous Investor-State Dispute Settlement (ISDS) schemes are part of virtually every existing trade deal and US corporations remain committed to the need for a legal process hidden from view.

Donald Trump’s new secretary of state, Rex Tillerson, won millions of dollars for ExxonMobil in secret arbitration deals when he was boss of the sprawling energy firm. Trump’s nominee for commerce secretary, Wilbur Ross, has already told Congress that he wants to present other countries with a “take it or leave it” trade model that includes stronger “enforcement mechanisms”, which very plausibly sounds like a more extreme version of the current secret courts system.

Peter Navarro, Trump’s chief trade adviser, also looks like he is spoiling for a fight on behalf of corporate America. It was Navarro, an economics professor and close pal of Ross, who hit the headlines last week after he accused Germany, Japan and China of being currency manipulators. In a paper with Ross before the presidential election, he argued strongly for tougher measures on imports to bring down Washington’s ballooning trade deficit.

None of this sounds like Britain will get the kind of easy ride promised by international trade minister Liam Fox and his equally naive colleagues Boris Johnson and David Davis. If anything, Fox will be forced to present parliament with a toxic cocktail of arrangements far worse than anything Brussels was prepared to demand.

Before the Brexit vote, EU officials reacted to public anger over ISDSs by putting forward a compromise deal. As EU commissioner Frans Timmermans said: “The new Investment Court System [ICS] will be composed of fully qualified judges, proceedings will be transparent, and cases will be decided on the basis of clear rules.”

Timmermans and his colleague, the trade commissioner Cecilia Malmström, managed to persuade the Canadians to include this new form of arbitration in the EU/Canada trade deal known as Ceta.

But even this will most likely be lost to the UK once it quits the EU. Last week, Fox was due to discuss the impact of Brexit on the Ceta deal.

Now Theresa May has decided that Britain is leaving the EU’s single market and customs union on current terms, all the UK’s trade deals via the EU will need to be renegotiated.

The hope among Brexiters has always been that the UK can strike a similar or improved compact with the countries covered by existing arrangements.

But the Canada deal explicitly recognises that arbitration will be overseen by the European Court of Justice (ECJ). The Brexit white paper says the UK will no longer come under the ECJ’s jurisdiction.

Once the UK leaves the EU, a new deal is almost certain to revert to the old ISDS system used by Canada, including in the Nafta agreement with Mexico and the US.

Fox said there wasn’t enough time to debate the fate of Ceta while the white paper was being discussed.

Eagerly, MPs turned to the white paper for an answer. But as Angus Armstrong, a senior director at the National Institute for Economic and Social Research points out, the white paper skirted the issue, even though it is pivotal to how trade disputes are decided in the future.

Nick Dearden, director of the campaign group Global Justice Now, said: “There’s every reason to suspect that any UK-US trade deal would involve something equal to, or even worse than, the system of ‘corporate courts’ or ISDS that proved to be so controversial in TTIP.”

Like many, Dearden, who advised voters last year against voting for Brexit to escape TTIP, fears a new deal will pave the way for massive US healthcare companies to mount a takeover of NHS services, and that chemically washed American chickens could supplant homegrown alternatives on supermarket shelves.

He has every reason to be concerned. While running Exxon, Tillerson launched investment disputes against a number of countries with which the US has treaties, including Venezuela and Argentina. Reports in the Canadian press show he brought a case against the country under Nafta that secured $17m in compensation for having to pay into a provincial research and development fund where Exxon drills for offshore oil.

No doubt Britain will suffer the same democratic deficit once Fox bends the knee in Washington.