British Prime Minister Theresa May on Friday issued the European Union (EU) with an ultimatum to come up with an alternative plan for Brexit and treat the UK with respect in the negotiations. Her televised statement from Downing Street came after a day of upheavals in Salzburg at Austria, during which European Council Head Donald Tusk announced that the UK's Brexit plans were unworkable. May hit back at the EU leaders for rejecting her plan with no alternative at this "late stage of negotiations", saying it was "not acceptable". "I will not overturn the result of the referendum nor will I break up my country," a defiant British PM said. "Yesterday Donald Tusk said our proposals would undermine the single market. He didn't explain how in any detail or make any counter-proposal. So we are at an impasse," she said. Her statement further noted: "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. "At this late stage in the negotiations, it is not acceptable to simply reject the other side's proposals without a detailed explanation and counter-proposals. So we now need to hear from the EU what the real issues are and what their alternative is so we can discuss them. Until we do, we cannot make progress." She said the two sides were still "a long way apart" on two big issues: the post-Brexit economic relationship between the UK and EU, and the "backstop" for the Irish border, if there is a delay in implementing that relationship. The two options being offered by the EU for the long-term relationship -for the UK to stay in the European Economic Area and customs union or a basic free trade agreement - were not acceptable, she said. May said the first option would "make a mockery of the referendum", while the second would mean Northern Ireland would be "permanently separated economically from the rest of the UK by a border down the Irish Sea." Reiterating her Brexit stand of "no deal is better than a bad deal", May said the best outcome would be to leave with a deal and the UK had put forward a third way - her Chequers plan, which Tusk rejected on Thursday on the ground that it would undermine the single market. The EU's statement had been received with a huge sense of shock in the UK, especially the Downing Street, as all hopes of a deal on May's Chequers plan were dashed by the leaders of the economic bloc. Fears of a no-deal Brexit, where the UK exits without a clear outline for a future relationship, are now likely to be seen as more real. The UK is due to leave the EU on March 29, 2019. May says her plan for the UK and EU to share a "common rulebook" for goods, but not services, is the only credible way to avoid a hard border between Northern Ireland and the Republic of Ireland. But it is opposed by some within her own party who argue that it would compromise the UK's sovereignty. And it seemed to have been dismissed at this week's EU summit in Austria. The markets reacted to the latest statement with the pound's fall against the dollar and the euro sliding more sharply.