Theresa May’s government is heading for the hardest of hard Brexits. That’s what many European officials now believe. In several capitals they have told me that – partly based on their reading of British newspapers – they think May is being pushed by the right of her party towards a deal that will achieve maximum sovereignty for Britain and do maximum damage to its economy.

They also reckon that, once the article 50 talks start, Britain will be in an extremely weak position. If no deal is struck within two yearson the exit settlement and any transitional arrangements, the UK goes over a “cliff edge”, with only World Trade Organisation rules for support. Service industries would then lack access to EU markets, while farmers and manufacturers would face tariffs. Such an outcome would cause discomfort for EU countries but be much more harmful to Britain: they take almost half of UK exports yet send it less than 10% of their own.

Michel Barnier, the European commission’s lead negotiator on Brexit, increased the pressure on Britain this week. He said that because of the time the EU would need to prepare for the talks and then ratify any deal, only 15 to 18 months would remain for proper negotiations.

Given such a weak hand, what can May hope to achieve? Staying in the single market is impossible, since she rejects free movement and the authority of the European court of justice (ECJ). Her best bet is to aim for a free trade agreement (FTA) (FTA) that provides zero tariffs on goods, plus some access to EU services markets.

Yet a half-decent agreement will require goodwill from Britain’s partners. And the government’s conduct in recent months has eroded that goodwill. May and her ministers need to rethink their style and tactics and then come up with substantive requests that generate a relatively warm response.

Michel Barnier, the European Commission’s lead negotiator on Brexit, has increased the pressure on Britain. Photograph: Thierry Monasse/AP

Ministers should be serious and courteous, while avoiding anti-EU rhetoric. To quote a senior official in one capital: “If you want a good deal, keep the negotiations boring and technical. The more your ministers grandstand, the more we become defensive and unhelpful.”

But not all ministers have got the message. When Boris Johnson said last month that the idea of free movement being a founding principle of the EU was “a total myth” and “bollocks”, he was both factually wrong and offensive. Nor does it help when the British make threats. Government sources have told newspapers that if the EU fails to offer a good trade deal, Britain will punish it by cutting corporation tax to 10% to lure overseas investors. That threat has simply ensured the EU will insist on the right to curb market access if Britain makes “unfair” tax cuts.

Britain’s partners also noted the media onslaught after the high court ruling on article 50; other governments thought it strange that ministers gave such halfhearted support to the principle of judicial independence. That episode did nothing for Britain’s reputation.

It would help if the prime minister made a big speech setting out a positive vision for what the UK could contribute to Europe post-Brexit. For instance, she could offer to make Britain’s expertise on foreign policy, defence, counter-terrorism and policing available to the EU, in pursuit of common policies and objectives. She could offer ships and border guards for policing and strengthening the EU’s external frontier – goals that would evidently benefit Britain. She could aspire to make Britain a closer partner of the EU on security policy than any other non-member.

May would also impress the 27 if she aimed for a high level of economic integration. She should make a clear commitment to a transitional deal to cover the several years that will elapse between Britain leaving the EU and the entry into force of an FTA. Businesses and financial firms are desperate for arrangements that could allow them a period in the customs union and parts of the single market while they consider their plans. May’s problem is that the EU’s price for the transition period will be politically unpalatable: free movement, ECJ rulings and budget payments.

The media onslaught after the high court ruling on article 50 did nothing for Britain’s reputation with its partners

May has not yet ruled out staying in the EU customs union in the long term, though UK officials think this is unlikely (countries in the customs union share a common external tariff on imports, but trade between them is tariff-free). It would mean that Britain would have to swallow EU trade policy, and that Liam Fox’s new department could not negotiate free-trade agreements with other countries.

But the case for remaining in the customs union is strong: many fewer bureaucratic delays and barriers at the UK-EU border, and minimal disruption of integrated supply chains (crucial for industries like cars and aerospace). Staying would also make it easier to avoid restoring controls on Northern Ireland’s border with Ireland. May should offer money for the funds that support the development of poorer EU members. Encouragingly, Brexit secretary David Davis has not ruled this out. If Britain made such payments – as Switzerland and Norway do – it would spur the EU to offer a more generous FTA.

The details of how Britain restricts free movement are important. If May offers a less stringent regime to EU citizens than to those from other nations – a policy backed by some of her ministers – she will earn goodwill. But if the new regime cuts the numbers of EU migrants sharply, goodwill will be lost. The 27 other nations, including Germany, would appreciate May consulting them on the details of the restrictions.

The 27 may be overly pessimistic in supposing it will be the hardest of Brexits. If the economy turns down sooner rather than later, the advocates of closer ties to the EU – including the Treasury and increasingly vocal business lobbies – will be strengthened. The parliamentary majority in favour of a soft Brexit may yet find a way of nudging government policy; this week ministers avoided a Commons defeat by backing a Labour motion requiring them to state their plans for the negotiation.

One of May’s strengths is that she believes in evidence-based policymaking. If she concludes that the national interest requires it, she may find the courage to break with the hard right and go for a not-so-hard Brexit.