The prime minister has been holding talks with Northern Ireland's Democratic Unionist Party, keen to get the backing of their 10 lawmakers in parliament to help her pass laws and govern as Britain starts talks to leave the European Union.
For Brussels, a concern with starting talks on such models would be that Brexit supporters might end up blocking them, raising the risk of time running out to get any deal: "Would you ..."
A week after May lost her majority in an election she had called in the hope of strengthening her hand in the talks, some fellow Conservatives want her to focus more on limiting the damage to business and less on cutting immigration and other ties to the European Union when Britain leaves the bloc in March 2019.
While the DUP are deeply eurosceptic, they have balked at some of the practical implications of a so-called hard Brexit - including a potential loss of an open border with the Republic of Ireland - and talks will touch on efforts to minimise the potential damage to Northern Ireland.
The EU has insisted that this sequence involve sorting out Britain's departure and urgent issues like the rights of citizens affected by Brexit before the shape of future ties or trade are discussed.
Former Conservative prime minister John Major has also raised doubts about the deal and its impact on the province's "fragile" peace, telling BBC radio that the government "will not be seen to be impartial" if locked into a deal.
London's neutrality is key to the delicate balance of power in Northern Ireland, which was once plagued by violence over Britain's control of the province.
An election in March saw the Protestant, pro-British DUP finish narrowly ahead of Catholic socialists Sinn Fein.
The discussions with the DUP were "productive talks", she added.
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Prime Minister May wants to negotiate the divorce and the future trading relationship with the European Union before Britain leaves in March 2019, followed by what she calls a phased implementation process to give business time to prepare for the impact of Brexit.
"The EU stands ready to begin negotiations".
But May's attempt to increase her majority in parliament were dashed and has weakened the government's negotiating position, with many arguing that May will have to take a softer stance and potentially seek some sort of access to the EU's single market.
"We haven't negotiated, we haven't progressed".
The EU meanwhile unveiled plans to give itself new powers over London's banking business after Brexit, in what could be a blow to the city's supremacy as a global financial hub. In a separate interview, she said the talks with the Conservatives had covered corporation tax and same-sex marriage.
"There is a unity of objective among people in the United Kingdom", May said following a meeting with French President Emmanuel Macron in Paris.
"As we enter negotiations next week, we will do so in a spirit of cooperation, taking a pragmatic approach, trying to find a solution that works both for the United Kingdom and the European Union 27", he told reporters before a meeting of the 28 EU finance ministers in Luxembourg.