The UK risks hurtling into “guaranteed no deal” if MPs fail to back a Brexit agreement at the end of a short extension period, according to senior EU sources.

Theresa May promised MPs on Tuesday that she would seek a “short, limited extension to article 50” beyond 29 March if parliament refuses to back her withdrawal agreement and votes against leaving without a deal.

Brussels insiders fear that scenario raises the risk of no deal in the summer. “It will be a no-return situation,” a senior diplomat told the Guardian. “If there is no solution [by the end of June] it is a guaranteed no deal.”

The midsummer crash landing would happen because the UK would not have taken part in European elections.

Most EU officials think 1 July is the last day the UK could remain an EU member state without having taken part in European elections. A three-month extension of article 50 to the end of June, coupled with missing the European elections in May, would make it legally impossible for the UK to continue as a member state, say official sources. The new parliament begins its work on 2 July.

“Three months maximum and then it’s clear for everyone that it is the only extension, the first and the last,” the diplomat said. “Then the UK would not have European elections, it would have to finalise everything.”

One senior official cautioned that it would be “very difficult” for EU leaders to agree to a short extension “if there is no clarity about how that would provide an agreement in the UK. If there is no clarity, it would be better to have a long extension.”

The EU is open to longer extensions, with various options mooted from nine to 21 months. The longer option, until the end of 2020, is seen by some senior EU insiders as a political tactic designed by the European commission to scare Conservative Eurosceptics into voting for the withdrawal agreement.

If the UK won an extension exceeding three months, it would have to be represented in the European parliament.

EU sources stress the EU has no fixed position on how long the Brexit extension should last. “We would pay a lot of attention to the business continuity argument,” the senior official said. “We have a number of important decisions this year and we cannot allow the mess of Brexit to pollute the decisions of the union.”

Brussels is sceptical that a divided Commons would find in three months the consensus that has eluded MPs for more than two and half years. “If people cannot agree now, why would it be possible in three months?” the diplomat said. “That being said, I don’t see that [EU27] heads of state and government would say no [to a three-month extension]. Probably they will say ‘let’s do that, let’s give them a last chance.’”

During a three-month extension period the EU would accelerate the no-deal planning, the source added.

European sources believe the last possible moment to clinch a Brexit deal, or an extension, will fall on 21/22 March, when EU leaders, including the prime minister, gather for a scheduled spring summit.

“The absolute deadline is the European council,” said another senior EU source, casting doubt on an 11th-hour agreement in the immediate days before 29 March, when the UK leaves the EU, with or without a deal.

Intense discussion on delaying Brexit came as the attorney general, Geoffrey Cox, arrived in Brussels on Tuesday for talks with the team of the EU’s chief negotiator, Michel Barnier.

“They held detailed technical discussions as part of the process ... to agree a deal that would have the support of the UK parliament and the EU,” a UK spokesperson said.

Cox was meeting EU officials in an attempt to pin down further assurances that would persuade MPs to back the Brexit deal they rejected by a historic majority last month.

Work is being pursued in three areas. First, the two sides are exploring changes to the non-binding political declaration that maps out the UK’s future relationship with the EU. The new version is expected to feature more details on workers’ rights and environmental protection, as May attempts to win over Labour MPs. But the government continues to rule out Jeremy Corbyn’s plan of a full customs union with the EU.

The second strand of work is focused on agreeing a process to agree “alternative arrangements” that could replace the contested Irish backstop. The backstop, a fallback plan to prevent a hard border on the island of Ireland, is part of the 585-page withdrawal agreement, which the EU has said is not open for renegotiation.

The EU has, however, promised to explore with the UK “alternative arrangements” such as technology and efficient customs procedures that could render the backstop unnecessary.

Tory Eurosceptic backbenchers hoping for a speedy agreement on those alternative arrangements are likely to be disappointed. Instead, negotiators hope to agree on a detailed timetable on the process for finding those alternative arrangements for the next 21 months.

The third area of work also seeks to quell MPs’ fears about the UK being “trapped” in the backstop. The EU is ready to add more legal weight to previous guarantees that the backstop is a last-resort option. A letter from EU leaders, Donald Tusk and Jean-Claude Juncker, released in January, could be turned into “a joint interpretative statement” – a document with greater legal heft that would be published in the EU rulebook, the Official Journal.