London CNN  — 

UK Prime Minister Theresa May said Friday that negotiations with the European Union were “at an impasse” after a disastrous summit at which her Brexit plan was largely rejected.

May struck a defiant tone during a Downing Street statement in which she called for the EU to “respect” the British position and the result of the June 2016 referendum.

A day after returning from the summit in Salzburg, Austria, she called on the EU to spell out its objections to her plan or come up with an alternative.

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

UK Prime Minister Theresa May, France's Emmanuel Macron, left, and other leaders at the summit.

Downing Street had hoped the informal Salzburg summit would pave the way to a resolution of outstanding issues in Brexit talks before a formal meeting in October. Instead, the leaders of the 27 remaining EU nations were unexpectedly resolute in their opposition to the UK leader’s proposals.

Donald Tusk, president of the European Council, said key aspects of the plan, agreed at the Prime Minister’s Chequers country retreat in July, “will not work” in their current form.

French President Emmanuel Macron went even further, saying that the entire Brexit project was sold to the British people by “liars” who immediately fled the stage, unwilling to see their project through.

In her Downing Street statement, May refused to budge and said the ball was in the EU’s court. “At this late stage in the negotiations, it is not acceptable to simply reject the other side’s proposals without a detailed explanation and counterproposals,” she said.

“So we now need to hear from the EU what the real issues are and what their alternative is so that we can discuss them. Until we do, we cannot make progress. In the meantime, we must and will continue the work of preparing ourselves for no deal.”

Tusk trolls May

May appeared bruised by the reception she got in Salzburg, and sounded particularly withering when referring to the European Council president. “Yesterday Donald Tusk said our proposals would undermine the single market. He didn’t explain how in any detail or make any counterproposal. So we are at an impasse,” she said.

Tusk drew attention Thursday for an Instagram post in which he appeared to troll May. An image of Tusk offering pastries to May is captioned: “A piece of cake, perhaps? Sorry, no cherries.”

The EU side has repeatedly accused Britain of wanting to “have its cake and eat it” and of cherry-picking as it seeks to keep elements of the single market it likes and ditch others it doesn’t.

Conservative lawmaker Charlie Elphicke condemned Tusk’s post as “extraordinarily disrespectful.”

In a statement Friday evening, Tusk said he “remained convinced that a compromise, good for all is still possible” and called the UK a close friend, adding he was a “true admirer of PM May.”

Speaking earlier Friday, May said the two sides remained “a long way apart” but insisted the British “stand ready” to work on resolving the issues.

The main sticking point continues to be how to handle the border between Northern Ireland, which will remain part of the UK, and the Republic of Ireland, which will continue to be part of the EU. Neither side wants an arrangement that would require the rebuilding of border infrastructure, the removal of which was a key part of the Good Friday Agreement that brought peace to Northern Ireland after years of sectarian strife.

May, whose Chequers plan proposes a common rulebook on goods and services to ensure that no customs checks are needed, insisted that creating any form of customs border between Northern Ireland and the rest of the UK was unacceptable.

“It is something I will never agree to – indeed, in my judgment it is something no British Prime Minister would ever agree to,” she said. “If the EU believe I will, they are making a fundamental mistake. Anything which fails to respect the referendum or which effectively divides our country in two would be a bad deal, and I have always said no deal is better than a bad deal.”

Troubles at home

Amid the uncertainty over the negotiations, May has been plagued by outspoken criticism from members of her own Conservative Party, in particular from ardent supporters of Brexit, who believe she has not been tough enough with the EU.

May will hope that her tough stance against the EU will insulate her from further criticism ahead of the Conservatives’ annual conference, which begins September 30.

Jacob Rees-Mogg, who chairs the powerful European Research Group, a fervently pro-Brexit caucus of Conservative members of Parliament, praised May for being “strong and forthright” in Friday’s speech. But he also demanded that she abandon her Chequers plan.

Meanwhile, “Remain” supporters have been rallying behind a burgeoning campaign for a new referendum, known as a “people’s vote.”

London Mayor Sadiq Khan, a vocal Brexit opponent, warned May’s statement moved the country “another step closer to the worst possible outcome from the Brexit negotiations – a catastrophic ‘no deal’ that would hammer jobs and economic growth.”

Khan, a member of the opposition Labour Party, urged the Prime Minister to change course. “Passing the buck to the EU to save her skin will not work,” he said.