DUP leader Arlene Foster has warned British Prime Minister Theresa May that she will withdraw her support in the House of Commons if Northern Ireland is given special EU and UK status after Brexit.

The warning came after reports that Northern Ireland could have a joint regime of UK and EU customs regulations, allowing it to trade freely with both, and a ten-mile wide "special economic zone" on the border to avoid checks there.

Ms Foster, who was speaking to Sky News, dismissed the suggestion and warned that parity with the rest of the UK was a "red line".

The DUP’s ten MPs support the Conservatives in Westminster under a confidence and supply arrangement.

She said: "For us, our only red line is that we are not treated any different from the rest of the United Kingdom, that there are no trade barriers put up between Northern Ireland and our biggest market which, of course, is Great Britain.

"That's what we will judge all of the propositions that are brought forward, we will judge it against that red line and she's very much aware of that, and I have confidence that she knows that she cannot bring forward anything that will breach that red line or we simply will not be able to support them."

Meanwhile, the UK’s Home Secretary has said that Britain will have a good set of proposals on Brexit policy ready for a meeting of European Union leaders later this month.

Sajid Javid said he expected a positive response from Brussels to those proposals.

Mrs May is struggling to find a proposal on post-Brexit customs arrangements - the biggest stumbling block so far in exit talks - to take into negotiations with Brussels as the clock ticks down to Britain's scheduled exit in March 2019.

British cabinet ministers were last month tasked with analysing the two main options so far put forward for the Irish border, a "customs partnership" proposal that would see Britain continue to collect tariffs on behalf of the EU and the technology-based "maximum facilitation" - or "max fac" - solution.

Brussels has already rejected both schemes, with chief Brexit negotiator Michel Barnier saying on Friday that neither was "operational or acceptable".

Minister for Foreign Affairs Simon Coveney said yesterday that Mrs May had two weeks to put forward workable proposals. 

Mr Javid said that discussions between ministers on agreeing a position were making good progress ahead of the EU summit at the end of June.

"I am absolutely confident as we get to the June council meeting that the prime minister will have a good set of proposals, and our colleagues in Europe will respond positively to them," Mr Javid told the BBC.

Speaking on the BBC’s Andrew Marr Show, he said the proposals would be in line with previous statements by Mrs May, and that a promised white paper policy document would be published in advance of the summit.

Elsewhere, Labour party backbencher Stella Creasy has renewed calls for a second Brexit referendum.

Ms Creasy made the call after a number of MPs signed an open letter to Labour leader Jeremy Corbyn urging him to change party policy.

Also speaking on the Andrew Marr show, she said: "Nobody's talking about rerunning the referendum, what we are saying is once you have a deal, once you know what leaving is like.

"The idea that only 650 people in this country, because they happen to be in Westminster, get to say whether that's what this country wants isn't right to us, so we think the public should have say now they know what leaving actually entails."

She added: "Whether you voted leave or remain, surely you would want to have a say."

Also today, the UK's shadow international trade secretary Barry Gardiner said that the British government's refusal to remain in a customs union with the European Union would ensure the UK was a "minnow trying to compete against whales" on the global stage.

Mr Gardiner told Sky News that Labour's Brexit policy would ensure "trade in goods would continue uninterrupted", adding: "The Tories' red line is actually going to make it much, much more difficult.

"They're the ones who will be isolated; they will be minnows trying to compete against whales.

"They will be a 70 million strong consumer market against America's 500 million."