The government will propose its plan to avoid a Brexit hard border with Ireland “next month”, the Northern Ireland secretary has said.

After a meeting with the EU’s chief negotiator in Brussels on Monday, Karen Bradley said the issue was a matter for “the whole cabinet” and that they would meet to discuss it.

The delay means the UK will only have three or four months to discuss its fully-formed “backstop” proposal with Brussels, with the deadline for a deal on withdrawal looming for October.

Theresa May is set to travel to Brussels on Thursday for a meeting with European leaders, but little movement on the issue is expected.

A previous plan unveiled earlier this month was criticised by Brussels as incomplete. Michel Barnier, the EU’s chief negotiator, said the British proposal would not prevent a hard border and would not be acceptable because of its time-limited nature.

Ms Bradley said she was in Brussels to explain “the sensitivities” of the Northern Ireland issue to Mr Barnier. The EU has suggested putting customs checks on Irish Sea ferries between Britain and Northern Ireland to prevent a hard border but Britain has rejected the idea.

Theresa May said earlier this year that “no British prime minister” would agree to such a state of affairs. Senior cabinet sources say the EU plan faces opposition from ministers across the board, while Ms May is under even more pressure to prevent the plan going ahead because she relies on the vote of Northern Irish unionists to have a majority in the House of Commons.

We’re working across cabinet ... to make sure that we can actually resolve the Irish border Karen Bradley, Northern Ireland secretary

The prime minister has, in theory, twice committed in writing to preventing a hard border on the island of Ireland but has rejected the EU technical proposal for avoiding it.

Speaking to the media after the meeting with Mr Barnier, Ms Bradley said: “It was an opportunity for me, as Northern Ireland secretary, to set out the position in Northern Ireland, the sensitivities in Northern Ireland and the need to make sure that we maintain that constitutional and economic integrity of the whole United Kingdom, and get a good deal for the whole United Kingdom, including the people of Northern Ireland.

“We’re working across cabinet on all matters to make sure that we can actually resolve the Irish border and no border down the Irish Sea through the overall UK relationship. That’s what we all want to achieve. But obviously we need to put into legal text those matters that were agreed in the joint report and that’s what we’re working on.”

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Tens of thousands of people demonstrated in London on Saturday calling for a second vote on Britain's departure from the European Union. / AFP PHOTO / Niklas HALLE'NNIKLAS HALLE'N/AFP/Getty Images NIKLAS HALLE'N AFP/Getty Images People's Vote march – demanding vote on final Brexit deal A young protestor shouts as she takes part in the People's Vote demonstration against Brexit Getty Images People's Vote march – demanding vote on final Brexit deal A woman holds a placard as she joins EU supporters, calling on the government to give Britons a vote on the final Brexit deal, participating in the 'People's Vote' march in central London, Britain June 23, 2018. REUTERS/Henry Nicholls HENRY NICHOLLS Reuters People's Vote march – demanding vote on final Brexit deal epa06833888 Pro-EU demonstrators take part in a People's March anti-Brexit rally in Parliament Square in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. 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The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal epa06833264 Thousands of people march through London during a People's March anti Brexit demonstration in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal Tens of thousands of people march through London EPA People's Vote march – demanding vote on final Brexit deal epa06833265 Thousands of people march through London during a People's March anti Brexit demonstration in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. 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The cabinet is expected to meet at the prime minister’s country retreat, Chequers, next month to hammer out agreement on the issue.