British Prime Minister Theresa May received a round of applause from European leaders on Thursday night, but there remain plenty of hurdles to overcome before the U.K. can leave the European Union (EU).

EU leaders are set to formally agree Friday to start the second phase of Brexit negotiations, mainly centered around trade talks.

At a summit dinner in Brussels, Belgium, on Thursday, May made a brief speech emphasizing the need for the U.K. and the EU to move forward together with negotiations. This was met with spontaneous applause from EU leaders.

European Commission President Jean-Claude Juncker said Friday that May was applauded because some “thought that indeed she did a big effort” to conclude phase one of the negotiations and “this needs to be recognized.”

However, analysts believe May will find future Brexit talks increasingly difficult.

“I expect very, very tough negations,” Zsolt Darvas, senior fellow at the Brussels-based think-tank Bruegel, told CNBC on Friday.

One of the issues set to dominate talks is the future of the financial services industry. “At the end, I think that access to financial services will be limited for U.K.-based firms and therefore a number of companies will relocate to the continent,” Darvas said.

At the moment, the City of London benefits from so-called passporting rights, meaning that U.K.-based companies can do business in any European country without requiring further authorization from each member state. It is expected that this right will be limited following the U.K.’s departure from the EU.

“I think there’s a strong willingness from the 27 to have a relatively free trade deal, but for services, especially financial services. EU leaders have said there’s not going to be cherry picking,” Darvas said.

“Thereby, the U.K. gets access to the financial markets of Europe, but at the same time the U.K. won’t accept European citizens to go and work in the U.K. as they currently do freely.”

The first phase of exit negotiations should have concluded in October, but only ended last week after a last-minute push to bring May’s junior coalition partner — Northern Ireland’s Democratic Unionist Party (DUP) — on board with the deal.

However, May told reporters in Brussels on Thursday that everything is “on track to deliver Brexit,” even though members of the British parliament voted Wednesday that the House of Commons must be given a vote on whether to accept the U.K.’s final deal with the EU.

Speaking on Friday, EC President Juncker left the door open to the U.K. staying in the EU, despite the ongoing discussions.

“That depends on the British parliament and the British people,” he said. “It’s not up to us to decide what the British have to do.”

The U.K. is set to leave the EU on March 29, 2019. Until then, negotiators have to conclude trade talks, agree on a transition period, and get parliamentary approval in several countries.