LONDON (Reuters) - Britain s Theresa May won a temporary reprieve from rival factions within her own party on Friday by striking a overnight agreement with the European Union that some business leaders hope will increase prospects of an orderly exit from the bloc. After all-night negotiations and an early morning dash to Brussels by May, she and EU Commission chief Jean-Claude Juncker agreed to start talking about trade and a post Brexit transition period, declaring  sufficient progress  had been made on the cost and detailed terms of the separation. This took some of the heat out of a conflict between Conservative lawmakers that had threatened May s fragile grip on the party s leadership, and eased pressure on her minority government from business leaders who have repeatedly warned of a post-Brexit exodus.  Everyone s won a reprieve here,  said Anand Menon, director of The UK in a Changing Europe think tank.  This isn t a deal, it s a progress report ... It s exactly what she wanted - all she wanted was progress.  The Conservative Party s historical divisions over Britain s relationship with the EU had threatened to erupt earlier in the week when a carefully choreographed announcement of a deal spectacularly collapsed after the small Northern Irish party propping up her government objected to the terms. That raised the prospect of a fourth successive Conservative prime minister being forced from power over a row about Europe - a flashpoint that played a major part in the downfall of David Cameron, John Major and Margaret Thatcher.  Pro-Brexit supporters said the only solution to the impasse over how to manage the Irish border after Brexit was to walk away from talks; pro-EU lawmakers said the deadlock could be better broken by agreeing to stay in the EU s customs union. In the end, they agreed that the details of the Irish border would be agreed as part of talks about the future relationship, according to a 15-page negotiators  report.  All we have done is put everything off until next year,  Menon said. But, influential voices from both sides of a party which still identifies along the  Leave  and  Remain  lines drawn during the June 2016 referendum, rallied round their leader, signaling a temporary truce. The agreement was endorsed by both Conservative Brexiteers and Remainers - both of which can count on enough supporters to undermine, and possibly even topple, May after her gamble on a June snap election backfired and stripped the party of a parliamentary majority.  This is a significant personal political achievement for the Prime Minister ... Earlier this week, there were all sorts of doomsayers who thought there would be no prospect of an agreement. They ve been proven wrong,  Michael Gove, an influential pro-Brexit member of her cabinet, told the BBC. In part, the closing of ranks around May reflects her party s concern that deposing her could trigger a fresh election in which a resurgent Labour Party, led by socialist Jeremy Corbyn, could win power. Former finance minister George Osborne, sacked by May in 2016, once described her pledge to run again as leader at the next election as something similar to seeing  the living dead in a second-rate horror film . On Thursday he predicted she would lose her leadership before the end of the current term, due to run until 2022.  Businesses also warmed to the declaration of progress, which was rubber-stamped over breakfast in Brussels after a night of back and forth phonecalls between May, her Northern Irish backers the Democratic Unionist Party, and EU officials.   Businesses will be breathing a sigh of relief,  said Adam Marshall, Director General of the British Chambers of Commerce.  The endorsements came with hefty caveats, warning that more clarity needed to come quickly to prevent businesses from triggering contingency plans to cope with a so-called  hard Brexit  in which Britain would leave without a negotiated settlement  The sand in the timer is running out - leave it too late and damage will be done to both the UK and the EU,  said Miles Celic CEO of the TheCityUK trade body which represents London s financial services sector.   For the financial and related professional services industry, our critical issues must now be progressed.  Equally, the calm among Brexiteers within May s party was not matched by those outside it, with one of the main campaign groups that persuaded Britons to vote 52 to 48 percent in favor of leaving saying she had not met their definition of Brexit. Much of their anger was directed at a backstop option set out in the text of the agreement which promised that if trade talks failed, the United Kingdom would maintain  full alignment  with those rules of the EU internal market and customs union that help protect north-south cooperation in Ireland.  Under Theresa May, we are leaving the European Union in name only,  said Leave campaigner Arron Banks in a statement.  If anyone in the Conservative Party has any integrity or sense of duty left, we call on them now to save Brexit by triggering a leadership contest.  Nevertheless, Friday s agreement was seen as a big step toward avoiding a chaotic exit and formalizing terms which would meet many pro-EU observers  definition of a  soft exit .  It means that  no deal  overall is less likely,  said Charles Grant, Director of the Centre for European Reform think tank. But the toughest part of the negotiations could be yet to come, with Britain looking to agree a huge free trade deal before March 2019 -  a tight timetable seen as unrealistic by Brussels.  In phase two it will emerge that the EU is going to give us a pretty bad deal in terms of what s in our economic interests,  Grant said.    Asked if Friday s agreement was a step toward a softer Brexit, May s spokesman said:  They re not terms that we ve ever recognized or engaged with. There is the Brexit, which the British people voted for, and that s what we re delivering.  