While May forms her Government, Brussels is impatient for Brexit negotiations

British Prime Minister Theresa May began talks on Tuesday to form an alliance with Northern Ireland's ultra-conservative DUP party in order to cling to power after her election fiasco, leaving the EU's Brexit negotiator wondering when divorce talks will begin.

Days after May lost her parliamentary majority in a failed electoral gamble, the premier welcomed the leader of the Democratic Unionist Party to Downing Street in a bid to gain the support of its 10 MPs.

May hopes with the backing of the DUP her Conservatives will again command the majority they lost in last week's election.

The arrival of the DUP's Arlene Foster followed a cabinet meeting, during which ministers went over plans "to deliver the best possible Brexit deal" according to a government spokeswoman.

Also on the cabinet's agenda were the talks to secure an alliance where the DUP back the Conservatives on a vote-by-vote basis in parliament, rather than a formal coalition government.

Before traveling to London, Foster on Monday said her party would go into the talks "with the national interest at heart".

The prospect of a deal has also caused consternation in Dublin, with Irish premier Enda Kenny warning such an alliance could upset Northern Ireland's fragile peace.

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.

May has dismissed calls to resign following the dismal election result and on Monday faced her MPs and vowed to govern.

"I got us into this mess, and I'm going to get us out," she told her Conservative MPs.

As May tried to manage the political fallout from the election, official data released on Tuesday showed inflation soared close to a four-year high in May.

Consumer Price Index inflation unexpectedly hit 2.9 percent last month, boosted by the rising cost of energy, food and recreational goods.

Brexit clock ticking

In calling a general election three years early, May had hoped to boost her slim majority ahead of Brexit talks starting later this month.

But a lackluster campaign saw her high approval rating slip away and support for her "hard Brexit" strategy — pulling out of the European single market and customs union — now hangs in the balance.

As May attempts to cobble together a majority, the EU's Michel Barnier said he would hold talks with British envoy Olly Robbins on Tuesday to organize the negotiations. 

"My preoccupation is that time is passing — it's passing quicker than anyone believes — because the subjects we need to deal with are extraordinarily complex from a technical, judicial and financial point of view. 

"That's why we're ready to start very quickly. I can't negotiate with myself," he told European newspapers including the Financial Times.

With the two-year clock on Brexit ticking away since March, when a letter from May formally started proceedings, Barnier dismissed the suggestion of postponing the negotiations and said such a delay would only prompt further instability.

The European Parliament's Brexit negotiator, Guy Verhofstadt, also expressed his frustration.

"We are impatiently waiting for the negotiating position of the UK gov(ernment). The current uncertainty cannot continue," he said on Twitter.

Verhofstadt also cast doubt on May's strategy, telling journalists at the parliament in Strasbourg that Britain's election result "was certainly not a support of the hard Brexit".

The EU meanwhile was preparing to unveil plans to give itself new powers over London's banking business after Brexit in a blow to the city's supremacy as a global financial hub.

The draft law will empower Europe to deny post-Brexit London the right to host financial market "clearing houses" that deal in euros, the EU's single currency, EU sources said.

May heads to Paris

Following London talks with the DUP, May will head to Paris to meet with French President Emmanuel Macron who has just won an impressive victory in the first round of parliamentary elections.

A working dinner between the British premier and her Europhile counterpart — a Brussels favorite — will be followed by their attendance at a friendly football match between England and France.

Colin Talbot, a professor of government at the University of Manchester, said the Paris trip is part of May's strategy to improve her position at home.

"Going abroad and being seen to be the prime minister and talking to the president of France, being seen to be wheeler-dealing on the international stage, is a classic move to shore up authority at home," he told AFP.

Macron and May are also expected to discuss the need for closer cooperation at the European level to fight terrorism, which they discussed at the G7 in Italy and at a NATO summit in Brussels late last month.

The two are proposing penalties including fines against tech companies that fail to remove extremist content. 

"I would expect that conversation to continue tomorrow. They may well discuss aspects of Brexit but the main focus will be on counterterrorism," May's spokesman said on Monday.