British Prime Minister Theresa May said on Friday Brexit talks with the European Union had hit an impasse, defiantly challenging the bloc to come up with their own plans a day after the bloc's 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 $1.3080, about 1.4 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 the 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." 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.

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.

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

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."

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