Leaders of Britain’s 27 EU partner countries have now thrown down the gauntlet: no discussions on a trade deal will take place until there’s progress on the UK’s divorce bill, the Ireland-UK border and the rights of EU citizens.

We are told there is a document on the table relating to UK citizens living in Europe and those of citizens from other EU countries who live in Britain, but the UK is not prepared to sign. No reason has been given as to why.

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The problem for our prime minister is that at every turn her head hits the hard wall of law and the role of the European court of justice (ECJ). Theresa May has cornered herself by insisting that the UK withdraw totally from the court and its decisions. Nobody explained to her that if you have cross-border rights and contracts you have to have cross-border law and regulations. And if you have cross-border law you have to have supranational courts to deal with disputes.

Call it what you like, but in the end you need rules as to conduct, and arbiters for disagreement. Even the World Trade Organisation has a disputes court.

But May has had a bellyful of European courts after her run-in with the totally separate European court of human rights when, as home secretary, she was trying to deport the fundamentalist preacher Abu Qatada to Jordan. Jordan’s use of torture on political opponents proved a handicap to his expulsion. However, although all this related to a quite separate legal regime, the words Europe and court in the same sentence still invite obstinate opposition from May.

This is now a problem in the Brexit negotiations, because all the preliminary matters raised by EU leaders involve legal commitments from which we cannot walk away. Calls to cut and run without paying a penny in the Brexit settlement are unlawful and unethical. It is not surprising that the other 27 want to see the colour of our money up front.

The law is under attack from Trump’s America to Poland, Hungary and Turkey. It is the currency of our dangerous times

There is talk of a special deal to be negotiated for Northern Ireland, whatever the rest of the UK does, by possibly joining the European Economic Area (EEA) with some additional border arrangements between Northern Ireland and the rest of the UK. EEA membership is a semidetached position that Norway, Iceland and Liechtenstein have signed up to, whereby they have the benefits of the EU single market but not the full obligations. However, it also has legal implications. You cannot trade without the protection of law because things can go wrong. EEA members have to sign up to the European Free Trade Association court, a special supranational judicial body which deals with EEA disputes; it sits in Luxembourg, and is run largely according to EU law and ECJ judgments. Of course, such law is made without the input of EEA states, which makes it a solution that would be hard for many Brexiteers to swallow.

In preparation for the negotiations, EU representatives have been appearing before Lords and Commons committees and meeting Brexit ministers. They are invariably bemused. They say they keep being told the UK wants to continue to be part of various arrangements, including the European arrest warrant and Europol – yet nobody in London seems to understand that such collaboration requires the ECJ to have ultimate jurisdiction and for EU law to apply.

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It seems obvious to them that cross-border collaboration requires supranational legal arrangements covering everything from financial services, trade, farming, fishing, security, environment, employment and maternity rights to industry standards and consumer rights. Intellectual property law, for instance, covers a huge array of research, entrepreneurship, invention and creativity; the European patent court has only recently been built here in London and was due to be opened. What happens to it now, they ask.

For years the British public have been subjected to a barrage of tabloid mendacity suggesting that we are victims of an onslaught of foreign-invented law and interference by foreign courts. In fact, a vast amount of incredibly advantageous law has been created in the EU in the past 40 years. And here’s the rub: we have been major contributors to that law. The British are good at law. We have had a strong hand in the creation of EU law.

The committee I chair in the House of Lords has heard overwhelming evidence about the benefits to business of being able, for instance, to secure a judgment in a British court against a recalcitrant debtor in Poland and know it will be enforced anywhere in the EU.

A mother can secure a maintenance order against her children’s renegade father who has sloped off to continental Europe, and have the order enforced. A holiday accident in Spain can lead to swifter resolution and compensation by virtue of EU law. A British father can get access to his kids by order of a court in Munich. Cross-border relationships require cross-border law, and agreements on mutual enforcement are fundamental.

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No wonder the European commission president, Jean-Claude Juncker, is reported to have said Theresa May is on another galaxy in imagining she can retain the best bits of Europe without its institutions or legal underpinnings. Her fantasy that the “great repeal bill” will fix the problem by bringing EU law home, or that a deal can be done without the need for any European court, is unravelling. These legal arrangements require reciprocity. The courts of EU countries do things for us because we do likewise for them. A piece of unilateral legislation on our part does not secure that mutuality which is embodied in many regulations.

Harmonising law across Europe has raised standards – to our advantage. Europe-wide law is integrated into our lives. In the “new order” of trade agreements with China and others, none of these safeguards will exist. My guess is that if May does secure a deal with the EU, we will find ourselves quietly signing up to a newly created court or tribunal, a lesser ECJ.

The law, judges and courts are under attack in many democracies – from Trump’s America to Poland, Hungary and Turkey. It is the currency of our dangerous times. Be warned: good law is a protection we have to preserve. The price of its loss will be very high indeed.