The EU is set to inflict a double humiliation on Theresa May, stripping Britain of its European agencies within weeks, while formally rejecting the prime minister’s calls for early trade talks.

The Observer has learned that EU diplomats agreed their uncompromising position at a crunch meeting on Tuesday, held to set out the union’s strategy in the talks due to start next month.

A beauty contest between member states who want the European banking and medicine agencies, currently located in London, will begin within two weeks, with selection criteria to be unveiled by the president of the European council, Donald Tusk.

The European Banking Authority and the European Medicines Agency employ about 1,000 people, many of them British, and provide a hub for businesses in the UK. It is understood that the EU’s chief negotiator hopes the agencies will know their new locations by June, although the process may take longer. Cities such as Frankfurt, Milan, Amsterdam and Paris are competing to take the agencies, which are regarded as among the EU’s crown jewels.

Meanwhile, it has emerged that Britain failed to secure the backing of any of the 27 countries for its case that trade talks should start early in the two years of negotiations allowed by article 50 of the Lisbon treaty. The position will be announced at a Brussels summit on 29 April.

Despite a recent whistlestop tour of EU capitals by the Brexit secretary, David Davis, diplomats concluded unanimously that the European commission was right to block any talks about a future comprehensive trade deal until the UK agrees to settle its divorce bill – which some estimate could be as high as €60bn – and comes to a settlement on the rights of EU citizens.

May will have hoped that draft European council guidelines, leaked last month, which took a tough line on the negotiations, including a clause ruling out a trade deal within two years, would have been softened during consultation with the member states. However, the lack of any questioning of the European commission’s position on the timeline surprised Brussels veterans, wearily used to displays of EU disunity.

The future prosperity of the of the single market was challenged. That had an impact – it pushed people together

Senior EU sources claimed that Britain’s aggressive approach to the talks, including threats of becoming a low-tax, low-regulation state unless it was given a good deal, had backfired. “However realistic the threats were, or not, they were noticed,” one senior EU source said. “The future prosperity of the single market was challenged. That had an impact – it pushed people together.”

Another senior diplomat said initial sympathy with Britain had fallen away in many capitals, due to the approach of Theresa May’s government. “Of course, we want to protect trade with Britain, but maintaining the single market, keeping trade flowing there, is the priority, and so we will work through [the EU’s chief negotiator] Michel Barnier,” the source said. “Britain used to be pragmatic. That doesn’t seem to be the case any more, and we need to protect our interests.”

It is understood that diplomats representing the right-wing Polish government voiced concerns about the rigid timetable for the talks in the private meeting on Tuesday, suggesting there were grounds for “flexibility”.

Facebook Twitter Pinterest Some have criticised Theresa May for adopting the ‘wrong tone’ on Brexit negotiations and leaving the UK at a disadvantage. Photograph: Andy Rain/EPA

Even then the intervention fell far short of backing the UK’s position that there could be parallel negotiations on the terms of withdrawal and the future relationship. A senior EU source said: “No one questioned the phased approach.”

In a further sign of Britain’s isolation, Spain’s right of veto over any future EU-UK deal applying to Gibraltar was not discussed on Tuesday, despite the UK’s anger over the issue, EU sources said. The contentious position is set to be waved into the final EU negotiating position by consensus.

French diplomats instead spent part of the meeting warning member states to help companies on the continent prepare for a scenario in which the UK crashes out of the EU without any deal or even transitional arrangement in place for after the country leaves the bloc in 2019, leading to tariffs and customs checks.

Keir Starmer, the shadow Brexit secretary, accused the government of wasting an opportunity where ministers should have been building bridges, as it approaches what have been billed as the most important negotiations the UK has ever faced.

He said: “It is deeply concerning that the prime minister is now so isolated from our EU partners. I have emphasised in parliament on a number of occasions that the tone adopted so far by the government is unlikely to get the talks off to a good start.

“The prime minister should have spent the last nine months building alliances across Europe, not pandering to those in her cabinet and her party who want to sever all links with the EU and retreat from our closest allies and most important trading partners.”

Gibraltar's future at stake in Brexit negotiations Read more

Liberal Democrat leader Tim Farron said: “April is set to be a humiliating month for May. Her choice to pursue a hard Brexit is starting to hit with reality and we are starting to see the impact that is going to have on Britain.”

The European commission said earlier this month that talks about a potential trade deal would occur only once “sufficient progress” had been made on Britain’s €60bn divorce bill and the position of EU citizens in the UK and British citizens on the continent.

It is understood diplomats representing the EU27 did discuss a definition of “sufficient progress”, but ultimately left it to the leaders to decide. An EU source said it was hoped that “scoping” talks on a deal, and a transitional arrangement on access to the single market, could start in the autumn.

The EU’s negotiating position detailed in the European council’s so-called draft guidelines will also be redrafted to include mention of the European parliament’s role, in a sign that MEPs are angling to play a greater part in shaping the talks.

Tusk’s team will “fine-tune” the guidelines ahead of a final meeting of diplomats on 24 April, an EU source said. A one-day summit of leaders will take place on 29 April in Brussels to sign off on the document.