BACK in October Theresa May promised to invoke Article 50, the legal procedure for leaving the European Union, by the end of March 2017. On March 29th the prime minister duly sent a six-page letter to Donald Tusk, the president of the European Council of heads of EU governments. Article 50 sets in motion a negotiating process with a two-year time limit that can be extended only by unanimous agreement of all EU governments. Mrs May told Parliament this was a time for the country to come together. And in her letter she promised her European partners (seven times) that she wanted a “deep and special partnership” with the EU.

No doubt mindful of the two-year deadline, the response from Brussels was swift. Mr Tusk issued a curt acknowledgment and said he would publish draft guidelines for the negotiations shortly. He confirmed that, after debate among EU governments, the European Council would meet on April 29th to approve the guidelines; later, governments will approve a negotiating mandate for the European Commission. The April meeting will fall between the two rounds of France’s presidential election, giving leaders something else to chew over. They will also have in mind Germany’s election in September.

A discussion that has so far mainly been among parties at home will now shift to the real battleground, between Britain and its EU partners. The British team will find that, for those partners, unity of the 27 is the main goal. Mr Tusk’s response says that the EU’s priority is to minimise uncertainty for “our citizens, businesses and member states”. And although the constructive tone of Mrs May’s letter was welcomed, many jibbed at her threat to link security and the fight against crime and terrorism to securing a trade deal.

The first tussle with Michel Barnier, a former French foreign minister who is the commission’s Brexit negotiator, will be over whether the talks should start with the terms of divorce and only later discuss a trade deal. This is what the European Council wants. Mrs May will argue that both issues should be negotiated simultaneously, since Article 50 talks of a settlement “taking account of the framework of [a leaving country’s] future relationship”. But the others are likely to stand firm.

Splendid integration

One reason for this is that the divorce talks alone will be difficult enough. The commission’s negotiating mandate will include agreeing on the rights of 3m EU citizens to stay in Britain and 1m Britons to stay in EU countries; finding some way to avert a hard border between Northern Ireland and the Irish republic; and settling the exit bill that it claims Britain must pay. The first should be uncontroversial, though it may take some time to settle. The second will be testing, because Britain’s plan to leave the EU’s single market and customs union seems to imply border controls. Yet it is the third that could be the most explosive.

The commission claims that past commitments plus future obligations mean that Britain owes the EU as much as €60bn ($65bn). It believes this debt could be enforced at the International Court of Justice. Mrs May’s letter refers to the matter only obliquely. David Davis, her Brexit secretary, likes to quote a report from the House of Lords citing legal advice that, after Brexit, Britain will owe the EU nothing. More fanciful Brexiteers even claim that the EU owes Britain money for its share in the capital of the European Investment Bank.

Rows over money have always been the bitterest of all in the EU. The departure of such a big net contributor will cause pain, one reason why the commission has talked up the size of the exit bill. The voting rules under Article 50 do not make Britain’s position any easier. The divorce settlement must be approved by a “qualified majority” of EU countries, excluding Britain, and by the European Parliament. The parliament’s Brexit point-man, Guy Verhofstadt, threatens to cause trouble.

There is a serious risk that the budget row will blow up the talks before they start. Mr Barnier has tried to avoid this by suggesting it is possible to agree to some broad principles for a settlement and leave the exact amounts for later haggling. That could take place when the discussion moves on to future trading arrangements. Alas, these could prove even harder to settle than the Article 50 divorce itself.

Mrs May has made clear that her priorities are to take back control of migration, breaching the EU’s principle of free movement of people, and to escape the jurisdiction of the European Court of Justice (ECJ). This means, as she accepts, that Britain must leave the EU’s single market and customs union. She rejects off-the-shelf models for a new trade relationship. Instead, she wants a bespoke free-trade deal that gives, to the maximum extent possible, barrier-free access to each other’s market.

This will be tricky to agree on, and even harder to ratify. In many countries the opponents of free trade will stand in the way. Negotiations take years: they started between Canada and the EU in 2007 and the resultant CETA deal is still not fully in force. The rules for approving a Britain-EU free-trade deal will be a problem, for as a “mixed” agreement it must be ratified by all national parliaments in the EU as well as some regional ones (including Wallonia’s, which almost kiboshed CETA).

Tangled up in red tape

Substituting new rules for those of the single market is even more complicated than agreeing on a free-trade deal, for they intrude into almost every part of business activity. A special number of the Oxford Review of Economic Policy gives an idea of the vast spread of policies that must be changed post-Brexit. Besides the economic and legal impacts, it includes chapters on a new migration regime, financial-services regulation, competition policy, regional aid, state aid, industrial policy, transport, agricultural support and higher education.

Against a tight deadline, the complexity of these issues will be a huge challenge. Anand Menon of King’s College, London, director of The UK in a Changing Europe, an academic network, reckons the Brexit negotiations will be the most difficult and complicated that any post-war government has faced. The Institute for Government, a think-tank, adds that Britain’s civil service is at its smallest since the war; it also notes gaps in the staffing of the relevant departments.

Trade negotiators insist a deal will take longer than two years. Some Brexiteers disagree, pointing out that, unlike normal trade talks, the two sides start in complete convergence, since Britain has been an EU member for 44 years. To cement this, they note that the misnamed Great Repeal Bill, promised by the government this week, will translate almost all current EU laws into British law. Yet it is not the starting point that matters, but what happens when a post-Brexit Britain freed from the ECJ begins to diverge from the EU’s norms.

In truth, the nub of the single market is not its scrapping of tariffs or even customs checks, but its getting rid of myriad non-tariff barriers thrown up by different rules and standards. The government is hinting that, for practical reasons, it might stick with some EU regulators (such as, perhaps, the European Medicines Agency) for some time after Brexit. But as Mujtaba Rahman of the Eurasia Group, a consultancy, says, this ducks the point that, if Britain wants to retain barrier-free access to the single market, it may have to observe all EU regulatory standards anyway.

Another argument from Brexiteers confronted by Article 50’s two-year deadline is that there is little to fear if there is no deal at all. Mrs May herself has insisted that “no deal for Britain is better than a bad deal for Britain”, though she did not repeat this in her letter. No deal means reverting to trade on World Trade Organisation terms. As Open Britain, another think-tank, notes, this implies not just all of the EU’s non-tariff barriers, but tariffs of 10% on cars, 15% on food and 36% on dairy products. It would end Britain’s access to the EU’s trade deals with 53 other countries. Last year the Treasury said this option would reduce GDP by 7.5% after 15 years. The House of Commons Foreign Affairs committee recently warned against the no-deal option.

If a comprehensive trade agreement cannot be made in two years, an obvious conclusion follows: some transitional arrangement will be needed after March 2019. Mrs May’s letter nods to this by talking about “implementation periods”. The trouble is that any such arrangement may itself be hard to agree on, especially if there is lack of clarity over the final destination. The simplest idea is to prolong the status quo, but that may be hard for Mrs May to sell at home if it entails both free movement of people and a role for the ECJ.

And then there are the implications for the United Kingdom. Some policies needing redesign post-Brexit, such as fisheries, are matters for devolved governments. This week the Scottish Parliament backed the demand of its first minister, Nicola Sturgeon, for a second independence referendum. In Northern Ireland, where attempts to form a new power-sharing executive have broken down again, Sinn Fein is calling for a referendum on whether to join the Irish republic. Mrs May has vowed to protect the “precious, precious union”, but she knows that both Scotland and Northern Ireland voted to stay in the EU last June.

At least she can take comfort in the ineffectiveness of the opposition at home. Both Labour and the UK Independence Party are beset by weak leadership and internal feuding. Yet her control over Parliament is not absolute. Her working majority is just 17. Passage of the Great Repeal Bill may be contentious, and it is only the first of up to 15 parliamentary bills necessitated by Brexit. Several MPs are loudly promising to hold Mrs May and Mr Davis to account over their Brexit promises. This week Sir Keir Starmer, the shadow Brexit secretary, produced six tests for judging if Labour should support the final deal, while a cross-party group under the auspices of Open Britain came up with ten points. The House of Lords, most of whose members are strongly anti-Brexit, may also make difficulties for Mrs May.

In the end, however, her biggest problem may not be with her opponents or with her EU partners across the negotiating table. As so many previous Tory prime ministers have found, it will be with her own backbenchers. Hardline Brexiteers are ready to denounce any compromise in the negotiations as a betrayal. Mrs May has raised their expectations, as well as those of voters, about the benefits of Brexit. When it becomes clear that there are costs instead, she may find her high popularity ratings fast withering away.