The EU is set to offer Theresa May a helping hand after her plan for a new meaningful vote was derailed, by formally agreeing on a new delayed Brexit date at this week’s summit and keeping it on offer until shortly before midnight on 29 March.

A change of the UK’s departure date in the draft withdrawal agreement – potentially from 29 March until three months later on 1 July – might convince the Commons Speaker, John Bercow, that the deal before parliament has changed, sources in Brussels suggested.

Bercow ruled on Monday that he would not permit a third attempt at passing May’s deal unless the offer to the Commons had fundamentally altered.

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The Brexit deal has been voted down twice, by 230 votes and 149. The guide to parliamentary procedure, known as Erskine May, suggests a question “may not be brought forward again during the same [Commons] session”.

But EU officials said they believed that issuing a summit communique with legal force, known as council conclusions, containing a new date of exit could be sufficient for another vote on the deal to be held.

The EU’s leaders are likely to suggest to May, who will need to agree to the offer when she meets in Brussels on Thursday, that there could be a three- or nine-month extension to the article 50 period if she manages to get her deal through parliament next week. The nine-month option would require the UK to hold European elections in May.

Should the prime minister advise the leaders that a bigger change to the deal is required by the Speaker, it is likely that the EU will insist on a nine-month extension or longer in order for the British position to evolve and negotiations to be advanced on the political declaration on the future deal. “That’s when it is in the hands of the leaders and we don’t know what they will do – anything up to 21 months extension, although I doubt that long,” said an official.

There is no certainty that a change of date will satisfy the Commons Speaker. But the EU will be available to sign off on the extension until the very last moment on 29 March, when the UK is currently set to leave, to give May the maximum amount of time to both persuade Bercow to hold the vote and then get it passed by MPs.

In the event of the prime minister failing to get her deal through the Commons before 29 March, the EU’s leaders are again likely to suggest that a nine-month option, or longer, remains open to her.

An EU diplomat said that the leaders would decide on the offer with May at the summit before remotely signing it off next week in a so-called “written procedure”, if and when another Commons vote is held.

There is no chance of the EU’s leaders meeting twice in the next few weeks to deal with the developments in British politics, EU officials said.

“We have to have all our procedures completed one hour before midnight Brussels time [11pm UK time]”, the diplomat said. “But everybody prefers to do it the formal way at the European council but from a legal point of view we have to say ‘yes’ a little bit before, not one minute to midnight. Everybody would prefer to have clarity as soon as possible on this because there will be a lot of consequences.”

The European commission secretary general, Martin Selmayr, had been pushing member states to limit an extension of article 50 up to 23 May to ensure there was no risk of the UK staying in the bloc without having elected MEPs. Senior EU sources said the bloc’s capitals had rejected the plan.

Earlier in the day, the British foreign secretary, Jeremy Hunt, arriving in Brussels for a meeting of EU ministers, said “a huge amount of work” was ongoing with Brexiters and MPs in the Democratic Unionist party to persuade them to back the deal.

“The risk of no deal, at least as far as the UK parliament is concerned, has receded somewhat, but the risk of Brexit paralysis has not,” he said. “That is not what people at home want; they want this deal to be sorted, they want us to get on and leave the EU in accordance with the referendum result. And that is why we will be redoubling our efforts.”

The failure to hold a meaningful vote this week does make it less likely May will be able to offer a clear reason for a Brexit delay of any length, raising the risk of leaders simply giving up on the prime minister, although the chances of that remain slim.

But several foreign ministers from the rest of the EU speaking in Brussels on Monday stressed they needed to know the next move in London before deciding on whether to extend the talks.

Belgium’s foreign minister, Didier Reynders, said the EU was awaiting a clear signal from London: “We are not against an extension in Belgium but the problem is, to do what?”

Lithuania’s foreign minister, Linas Linkevičius, regretted that there was “no vision, no clarity” from the UK on Brexit, just three days before a crucial summit.

He said it was “really important for our UK colleagues to reset [the] mindset and to look for exit from this stalemate situation because it is really not good for all”.