LONDON (Reuters) - British Prime Minister Theresa May said on Friday that Brexit talks with the European Union had hit an impasse, defiantly challenging the bloc to come up with its own plans a day after EU leaders savaged her proposals.

At a summit in Austria on Thursday, EU leaders rejected May’s “Chequers” plan, saying she needed to give ground on trade and customs arrangements for the UK border with Ireland.

The British media said the response had left her proposals in tatters, and May angrily struck back in a televised address from her Downing Street office, saying neither side should expect the impossible from the other.

“Throughout this process, I have treated the EU with nothing but respect,” May said. “The UK expects the same. A good relationship at the end of this process depends on it.”

Sterling extended its losses as May spoke, falling to as low as $1.3053, and was down around 1.5 percent on the day, putting it on course for its biggest one-day drop this year, over growing fears Britain could leave the EU without any deal.

May has said her Chequers proposals for trade with the EU, which would resolve arguments over the border of Northern Ireland with the Irish Republic, were the only way forward. EU leaders in Salzburg repeated their view that the plans would undermine their cherished single market.

After the summit, EU leaders said they would push for an agreement next month, but both sides have warned they are planning for a no-deal scenario.

“It’s not acceptable to simply reject the other side’s proposals without a detailed explanation and counter proposals,” May said. “So we now need to hear from the EU what the real issues are, what their alternative is, so that we can discuss them. Until we do, we cannot make progress.”

In Brussels, European Council President Donald Tusk said after May’s comments he was convinced that the European Union and Britain could still find a compromise.

“While understanding the logic of the negotiations, I remain convinced that a compromise, good for all, is still possible,” he said in a statement. “I say these words as a close friend of the UK and a true admirer of PM May.”

May, who commands a majority in parliament only with the support of a small pro-Brexit Northern Irish party, said she could not agree to any deal which treated Northern Ireland differently to the rest of the United Kingdom.

Arlene Foster, the head of Northern Ireland’s Democratic Unionist Party which supports May’s government, welcomed May’s tough stance against “disrespectful, intransigent and disgraceful” behaviour by the EU.

She said her party would veto any attempt to introduce a new regulatory barrier between the region and the rest of the United Kingdom.

The EU insists that there can be no hard border between the British province and the Irish Republic, with Northern Ireland remaining in the bloc’s customs union or effectively establishing a border in the Irish Sea if no alternative deal is reached.

“WE STAND READY”

“I will not overturn the result of the referendum nor will I break up my country,” she said. “We need serious engagement on resolving the two main problems in the negotiations and we stand ready.”

However, she said no matter what happened, the rights of three million EU citizens living in the United Kingdom would be protected.

Slideshow ( 9 images )

Earlier, her Brexit Secretary Dominic Raab said some EU leaders had shown unstatesmanlike behaviour in Salzburg.

“We’ve already compromised hugely with the Chequers proposals,” Raab told BBC TV. “What we’re not going to do is be salami sliced throughout this negotiation in a typical style that the EU engages in without movement on the other side.”

For the British media, the message from Salzburg had been clear. “Your Brexit’s broken,” the Daily Mirror newspaper said.

Newspapers led their front pages with a Reuters picture showing May, dressed in a red jacket, standing apparently aloof and alone from a mass of suited male EU leaders.

Slideshow ( 9 images )

May faces a fight with angry Conservative lawmakers at her party’s annual conference from Sept. 30.

Many have voiced opposition to her plans, which they said would bind Britain into much EU regulation in return for free trade, and some would prefer a no-deal “hard Brexit” in March, despite warnings that would ravage the British economy.

“Theresa May’s Brexit negotiating strategy has been a disaster,” opposition Labour leader Jeremy Corbyn said. “The Tories have spent more time arguing among themselves than negotiating with the EU.”

“The political games from both the EU and our government need to end because no deal is not an option.”

Scottish First Minister Nicola Sturgeon called May’s statement “dreadful” and warned that May’s party would pay a high political price if there was “no deal”.

In response to May’s statement, the Confederation of British Industry and other business bodies said they wanted to see constructive dialogue, not rhetoric.

Last week, London Mayor Sadiq Khan added his voice to those including union and business leaders who said there should be a second Brexit referendum. Scotland’s top court ruled on Friday that the European Court of Justice should consider whether Britain could unilaterally change its mind on Brexit.

“The referendum was the largest democratic exercise this country has ever undergone,” said May, who has repeatedly ruled out a second vote following the original 2016 referendum. “To deny its legitimacy or frustrate its result threatens public trust in our democracy.”