SALZBURG, Austria (Reuters) - Prime Minister Theresa May appealed directly to fellow European leaders on Wednesday to drop “unacceptable” Brexit demands that she said could rip Britain apart, and urged the bloc to respond in kind to her “serious and workable” plan.

Over Wiener schnitzel in Salzburg, May tried to win over the leaders of the European Union by effectively asking them what they would do if they were asked to agree a “legal separation” of their countries -- something she says the EU is asking for by insisting Northern Ireland might stay under EU economic rules.

It may be a high-risk strategy. EU officials again said Britain had to move its own position over what has become known as the Irish backstop - how to avoid erecting border posts between the British province and EU member Ireland - as well as on future economic cooperation after Brexit day in March.

A government source suggested Britain would come up with other proposals to try to reach agreement on Northern Ireland “in due course”, but May has so far been reluctant to move from her Chequers plan, hashed out at her country home in July.

With just over six months to Brexit day, both sides agree on one point - that time is running out to secure a deal that will mark Britain’s biggest policy shift in almost half a century.

“I believe that I have put forward serious and workable proposals. We will of course not agree on every detail, but I hope that you will respond in kind,” she told the other leaders at the Felsenreitschule theatre -- known to film fans for a scene in the musical ‘The Sound of Music’.

“The onus is now on all of us to get this deal done,” she said, according to the senior British government source.

BORDER PLAN “NOT CREDIBLE”

The talks, which have gone on for over a year, are bogged down in how to ensure that what will become Britain’s only land border with the EU, between Northern Ireland and Ireland, will not become home again to the checks and tensions of the past.

May has rejected an EU proposal to keep the province in a customs union with the bloc if they fail to reach a deal to keep the entire EU-UK border open, instead offering a time-limited customs arrangement that would cover the whole of Britain.

Over dinner, she said the problem could be solved by securing the type of “frictionless trade” envisaged in her Chequers plan, and that Britain was still committed to agreeing a fall-back scheme with the EU.

“However, the Commission’s proposal for this protocol - that I should assent to a legal separation of the United Kingdom into two customs territories - is not credible,” she said.

May has shown little sign of moving away from her Brexit plan, shrugging off criticism not only from Brussels but also at home over her proposals for future trade relations and Northern Ireland.

Slideshow ( 7 images )

She may have little option. Facing the annual Conservative Party conference later this month, she is keen to show hardline Brexiters who have called on her to “chuck Chequers” that her plan is the only one that can be negotiated with the EU.

And, possibly for that audience, she told the EU leaders that although time was short, “delaying or extending these negotiations is not an option” and rule out the option of a second referendum on Britain’s EU membership.

EU officials are minded not to paint May into a corner, aware of the increasing opposition to her plans in her Conservative Party, and that she needs a victory of sorts to persuade a reluctant parliament to back a deal.

Slideshow ( 7 images )

But while they were keen to emphasise the positive movement seen in the Chequers plan, some said no deal could be reached until there was movement from Britain on Northern Ireland.

“NO PROGRESS”

Irish Prime Minister Leo Varadkar told reporters there had been no advance on the issue: “I don’t think we’re any closer to a withdrawal agreement than we were in March, so I can’t report any progress, unfortunately.”

European Commission President Jean-Claude Juncker said a deal with Britain was still “far away”.

According to an EU official, chief negotiator Michel Barnier has suggested going to the “bare bones” on any checks between the rest of Britain and Northern Ireland, which could be further reduced if there is a trade facilitation agreement similar to that with Japan.

The government source said Britain had yet to receive a formal proposal.

But he did say London would offer proposals for regulatory aspects of the backstop to try to move the talks forward. He did not say when. EU negotiators say the problem is not only about customs but also ensuring the goods coming into the EU are produced according to EU rules, which Britain wants to shed.

May expects little immediate feedback at the dinner.

She will attend a morning session on Thursday to discuss security, where she will raise the poisoning of a former Russian spy in Salisbury. She will also have a face-to-face meeting with Varadkar.

She will then be out of the room when the other 27 leaders discuss her Brexit proposals over lunch, and will find out about their reactions only when Tusk briefs her separately afterwards.

But the senior British source said Britain believed momentum was growing for a deal, noting Tusk’s plan to convene a special summit in mid-November to ink a hoped-for treaty.

“I think this signals that very serious discussions are now taking place,” the source said. “We are confident of getting a deal.”