An infuriated but still calm Prime Minister Theresa May told the British public that Brexit negotiations with the European Union (EU) are deadlocked and there will be no progress until the EU treats the United Kingdom's proposals seriously.

May accused EU leaders that met recently in Salzburg, Austria of being dismissive of the UK after they dismissed her Chequers plan without any alternative or explanation. In an irritated tone of voice, May said it's not acceptable to simply reject Britain's proposals without a detailed explanation and counter-proposals.

She said Britain now needs 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 previously said her Chequers proposals for trade with the EU would have resolved arguments over the border of Northern Ireland with the Irish Republic. She told EU leaders her Chequers blueprint is the only way to implement Brexit. Chequers will also ensure a "deep and special partnership" with the EU in the future.

EU leaders in Salzburg demurred, repeating their view that Chequers will undermine the single market that is the European Union. They said the Chequers plan is unworkable since it will fragment the single market.

They insist there can be no hard border between Northern Ireland (a British province) and the Irish Republic (an independent state), with Northern Ireland remaining in the bloc's customs union. There can also be no border in the Irish Sea if no alternative Brexit deal is reached.

After the summit, EU leaders said they intend to push for a Brexit agreement next month. Both sides, however, are bracing for a no-deal scenario.

European Council President Donald Tusk said after May's comments he remains convinced the EU and the UK can still find a compromise way forward.

The summit of EU leaders in Salzburg on Sept. 20 was supposed to help bridge intractable differences and pave the way for a Brexit deal by the middle of November at the latest. Political pundits have noted that Salzburg has, instead, driven a wedge between the UK and the EU. May is also accusing the EU of bad faith and "un-statesmanlike" behavior.

In her TV address, May said the two sides remain "a long way" apart on the crucial issues of how the UK will trade with the EU after Brexit and the future of the border between Northern Ireland and the Republic of Ireland.

May further rejected the two options proposed by the EU -- a Norway-style association agreement and a more liberal relationship based on Canada's trade deal with the EU.