Britain rejects the EU's proposed solution - to keep Northern Ireland inside the bloc's single market and customs union after the rest of the UK leaves - because it would create new barriers between Northern Ireland and the rest of the UK The EU has asked for a counter-proposal from Britain.

The British prime minister is fighting on multiple fronts amid signs that some of her cabinet could walk out next week over the backstop, her insurance plan to keep the Northern Ireland border open.

Britain's worldwide trade, environment and Brexit ministers told May at a meeting on Thursday that they fear the whole of Britain could remain in the EU customs union for an open-ended period, the BBC said.

Prime Minister Theresa May relies on her DUP allies' 10 MPs to prop up her minority Government in key votes and there have been suggestions the Northern Irish party could vote against the Budget.

The Guardian said House of Commons leader Andrea Leadsom was also concerned about May's reported plan to accept keeping Britain in the EU customs union for an indefinite period after it withdraws.

The DUP vehemently opposes any checks between Northern Ireland and mainland Britain after Brexit, which is due in March and would be the United Kingdom's biggest trade and foreign policy shift for more than four decades.

Several eurosceptic ministers are now reportedly considering resigning over plans to give ground on the so-called backstop arrangement.

"But it is true that there needs to be a period, probably following the transition period that we have negotiated, before we enter into our long-term partnership, just because of the time it will take to implement the systems required", he said.

Brexit supporters accept there is likely to be some short-term economic pain but say the government is trying to scare voters about the impact of a no-deal exit.

Work and Pensions Secretary Esther McVey, who was not at the Downing Street meeting, has pointedly refused to endorse the Prime Minister's Chequers blueprint for Brexit.

He pointed out that the parliament will only be voting on the framework of a future trade deal with the European Union before March next year.

In an effort to find a way to avoid a hard border, reports have suggested the United Kingdom could remain tied to Brussels' rules beyond the end of 2020 to give negotiators more time to finalise an overall trade deal.

Merkel, who was in the Netherlands for talks with Rutte ahead of next week's meeting, said that she is pleased intensive discussions are now taking place.

Ahead of a crucial summit of European Union leaders next week, May "briefed her inner cabinet. that a historic Brexit deal is close", the Financial Times reported on Thursday.