Theresa May fired a warning shot at Brexit supporters on Tuesday, insisting there was “no suggestion” Britain would leave the EU without an insurance provision to protect against a hard border in Northern Ireland.

At a speech in Belfast, May would only accept that technology could “play a part” in any alternative arrangements and that she would not countenance anything that would disrupt the lives of border communities.

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Brexit supporters immediately expressed their alarm at some of May’s language, which they fear could be read as a step back from previous assurances. “She knows what she promised us,” one ERG source said. “Even if she didn’t mean what she said, we do.”

The comments came as May prepared to meet EU leaders in Brussels for the first time since the historic defeat of her Brexit deal, where she is expected to formally request the reopening of the withdrawal agreement in order to address concerns about the backstop.

The prime minister will travel to the Belgian capital on Thursday, meeting the European commission president, Jean-Claude Juncker, the EU parliament president Antonio Tajani, and the European council president. Donald Tusk. Both Tusk and Juncker have been adamant that the withdrawal agreement will not be reopened.

Number 10 sources suggested they did not expect a warm reception, but that it would signal the start of a new diplomatic process, involving proposals on the backstop worked on by MPs and ministers.

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Earlier on Tuesday, May told her cabinet she would not countenance any delay to the UK’s exit on 29 March, a message to ministers such as Jeremy Hunt and Sajid Javid who have suggested at least some delay might now be inevitable. Ministers who are more pessimistic about the prospects of the UK leaving on time with a deal held their tongues in the meeting after May’s warning.

“She was pretty clear she had no time for anyone calling for it to be extended,” one cabinet source said.

However, senior government sources increasingly believe the impasse may not be resolved until March, given no full EU council summit is due until late that month. That may ultimately become an excuse, some believe, for the prime minister to delay the UK’s exit in order to finalise any compromise.

In cabinet, ministers including Amber Rudd and Michael Gove are understood to have underlined how they did not believe the UK public had fully comprehended the severe damage no deal would do.

May did not set out explicitly to her cabinet the changes she would seek when she meets EU leaders.

However, speaking in Belfast, May said she knew there were anxieties in Northern Ireland about replacing the backstop arrangement and said there would always be an insurance option to prevent a hard border contained within the withdrawal agreement.

“I’m not proposing to persuade people to accept a deal that does not contain that insurance policy for the future,” she said.

“There is no suggestion that we are not going to ensure that in the future there is provision for this – it has been called an insurance policy, the backstop – that ensures that if the future relationship is not in place by the end of the implementation period, there will be arrangements in place to ensure that we deliver no hard border.”

Earlier in her speech, May also sounded a note of caution about the alternative arrangements that some MPs have been working on to replace the backstop. She said a seamless border was “the cornerstone around which the community in Northern Ireland has come together to deliver peace and prosperity”.

“I will not do anything to put that at risk,” she said. “So while I have said that technology could play a part, and that we will look at alternative arrangements, these must be ones that can be made to work for the particular circumstances of Northern Ireland.”

Tory MPs from a number of different Brexit factions are working on a proposal for alternative technological arrangements to the backstop, known as the Malthouse compromise after the housing minister, Kit Malthouse, who brought the groups together.

Members of the European Research Group, which is made up of Eurosceptic Tory backbenchers, agreed to back a compromise amendment last week on changes to the backstop after assurances from May that it would mean reopening the withdrawal agreement.

Downing Street would not say if work by the Brexit secretary Steve Barclay, who is working with Conservative backbenchers on the Malthouse compromise, would conclude by the end of Wednesday.

The attorney general, Geoffrey Cox, is also drawing up a proposal on legally binding limits to the backstop.

At her speech in Belfast, May said she would never allow a hard border to be erected on the island of Ireland.

“Northern Ireland does not have to rely on the Irish government or the European Union to prevent a return to borders of the past,” she said at a speech in Belfast. “The UK government will not let that happen. I will not let that happen.”

May said she understood that the “prospect of changing the backstop and reopening the withdrawal agreement creates real anxiety” in Northern Ireland but it was necessary to get the deal through the Commons.

The audience of Northern Ireland business owners and executives gave lukewarm applause to her speech. Several said they were frustrated that her plan to avoid a hard border and disruption to trade remained unclear.

Aodhán Connolly, director of the Northern Ireland Retail Consortium, said he hoped a meeting with May after her speech would clarify how she intended to reconcile promises on the backstop with avoiding a hard border.

“You’re talking about the disintegration of the supply chain. Northern Ireland is in the eye of the storm,” he said.