Fighting back tears, Theresa May said on Friday she would quit, setting up a contest that will install a new British prime minister who could pursue a cleaner break with the European Union. May bequeaths a deeply divided country and a political elite that is deadlocked over how, when or whether to leave the EU. The latest deadline for Britain's departure is Oct. 31. Most of the leading contenders to succeed May want a tougher divorce deal, although the EU has said it will not renegotiate the Withdrawal Agreement it sealed with Britain in November. Spain said it now seemed almost impossible to avoid a so-called hard Brexit, or clean break from the EU, and the bloc signalled there would be no change on the agreement despite European Commission President Jean-Claude Juncker learning of May's resignation "without personal joy". Irish Foreign Minister Simon Coveney underlined the bloc's stance that there would be no better Brexit deal. "This idea that a new prime minister will be a tougher negotiator and will put it up to the EU and get a much better deal for Britain? That's not how the EU works," Coveney told Ireland's Newstalk radio station. Sterling swung back and forth on May's resignation, trading slightly higher on the day, and British government bond yields edged off near-two-year lows struck first thing on Friday. Boris Johnson, the face of the official Brexit campaign in 2016, is the favourite to succeed May and he thanked her for her "stoical service". Betting markets put a 40% implied probability on Johnson winning the top job.