British Prime Minister Theresa May said Friday the European Union must come up with an alternative to her Brexit proposals, noting that talks had reached an impasse after bloc leaders had rejected her plans without explaining why.

"It's not acceptable to simply reject the other side's proposals without a detailed explanation and counter proposals," May said in a televised statement.

"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."

At a summit in Austria on Thursday, EU leaders said they would push for a Brexit deal next month but rejected May's so-called Chequers plan, saying she needed to give ground on trade and arrangements for the UK border with Ireland.

May said she could not agree to any deal that treated Northern Ireland differently than the rest of the United Kingdom.

"I will not overturn the result of the referendum nor will I break up my country," May told broadcasters from Downing Street. "We need serious engagement on resolving the two main problems in the negotiations and we stand ready."

For the British media early Friday, the message was clear after the Salzburg summit.

"Your Brexit's broken," the Daily Mirror newspaper said on its front page.

May and European Commission President Jean-Claude Juncker were among those attending the EU leaders' informal summit in Salzburg, Austria, on Thursday. (Leonhard Foeger/Reuters)

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

"May humiliated," the Guardian newspaper said.

"May's Salzburg hopes dashed as EU leaders reject Chequers deal," said the Financial Times, which has strongly supported EU membership.

'EU Dirty Rats'

The negative headlines indicate the extent of the divergence in perceptions between London and the capitals of the EU's other 27 members on the future of Brexit.

The Sun went much further: "EU Dirty Rats — Euro mobsters ambush May," it said alongside a mocked up picture of French President Emmanuel Macron and European Council President Donald Tusk cast as American gangsters with guns.

Macron bluntly said May's Brexit proposals, known as Chequers after the country house where they were agreed by the British cabinet in July, were "unacceptable."

May will emerge as unique in the annals of history if she survives as PM much longer in the face of setbacks on this scale. - Robert Peston, journalist

Tusk was criticized for posting a picture of him offering May a choice of delicate cakes beside a message: "Sorry, no cherries." That is a reference to what EU leaders cast as British attempts to cherry pick elements of EU membership.

European Commission President Jean-Claude Juncker sought to calm any hurt feelings but called for caution, comparing Britain and the EU to two loving hedgehogs.

"When two hedgehogs hug each other, you have to be careful that there will be no scratches," he told Austrian newspapers.

A number of British newspapers carried this image of May standing near EU leaders at the summit, in a veiled reference to the chilly reception to her Brexit plan. (Lisi Niesner/Reuters)

Britain is due to leave the European Union on March 29, yet little is clear. There is, so far, no divorce deal, rivals to May are circling and some rebels have vowed to vote against a possible Brexit deal.

Both London and Brussels say they want a divorce deal, though there is limited time if the British and EU parliaments are to ratify a deal by March 29. Any deal must be approved by British lawmakers.

The Spectator used the headline: "Chequers goes pop: Theresa May's Salzburg catastrophe."

"May will emerge as unique in the annals of history if she survives as PM much longer in the face of setbacks on this scale," British journalist Robert Peston wrote.

DUP's Foster backs May

On Thursday, May promised new proposals to reassure Dublin that it would not get a "hard border" with Northern Ireland but said she too could live with a no-deal outcome.

May's stance won praise on Friday from the head of Northern Ireland's Democratic Unionist Party, whose party has helped the Conservatives retain a majority in Parliament.

"Any new regulatory barrier would be a matter for the Northern Ireland Assembly, where the DUP would veto any attempt to undermine the economic or constitutional integrity of the United Kingdom," said Arlene Foster.

May and Arlene Foster are shown July 19 in Fermanagh, Northern Ireland. Foster reacted angrily Friday to the idea of a regulatory barrier between Northern Ireland and the rest of Britain. (Clodagh Kilcoyne/Reuters)

"The prime minister is right to stand firm in the face of disrespectful, intransigent and disgraceful behavior by the European Union," Foster added in a statement. "The United Kingdom will not be treated in such a manner."

Foster's support notwithstanding, May's former Brexit minister, David Davis, has said up to 40 lawmakers from the Conservative Party will vote against her Brexit plans.

Davis told Huffington Post there was a "rock solid" core of party lawmakers who belonged to the European Research Group, a grouping that wants a sharper break with the EU and was willing to vote down her plans.

If a possible deal were rejected by the British Parliament, Britain would face leaving the EU without an agreement, delaying Brexit or calling another referendum.

"If all conventional roads lead to a hard no-deal Brexit, the notion of Parliament exerting control and forcing another referendum on us would begin to look not wholly fanciful," Peston wrote in the Spectator.

If it left without a deal, the country would move from seamless trade with the EU to customs arrangements set by the World Trade Organization for external states.

Many business chiefs and investors say a so-called no-deal Brexit would weaken the West, panic financial markets and block the arteries of trade. Brexit supporters say such fears are exaggerated and Britain would thrive in the long term.