* Weak Conservative government may raise risk talks collapse
* EU had hoped stronger May could cut compromise deals
* EU doubts British could accept terms of "soft Brexit" (Adds new Juncker, Tusk quotes, May on talks in 10 days)
BRUSSELS, June 9 (Reuters) - European Union leaders fear Prime Minister Theresa May's shock loss of her parliamentary majority raises the risk of failure in Brexit negotiations due to start this month that will usher Britain out of the EU in March 2019.
There was concern that a weak minority administration and a possible leadership challenge to May after her electoral gamble backfired might mean further delay to the start of talks scheduled for June 19. But the prime minister said her new government would now prepare for discussions in 10 days time.
However, Guenther Oettinger, the German member of the EU executive, was among those warning that a weak British leader may be a problem once talks start. "We need a government that can act," he told German radio. "With a weak negotiating partner, there's a danger the negotiations will turn out badly."
Oettinger's boss, European Commission President Jean-Claude Juncker, said his Brexit negotiating team under Michel Barnier was ready: "The clock is ticking," Juncker said.
Barnier sounded conciliatory: "Brexit negotiations should start when UK is ready," he tweeted. "Timetable and EU positions are clear. Let's put our minds together on striking a deal."
Donald Tusk, the former Polish premier who will oversee the process as chair of EU national leaders' summits, also stressed there was "no time to lose" and a need for London and Brussels to cooperate to minimise disruption for people, businesses and governments across Europe when Britain walks out in 22 months.
"Our shared responsibility and urgent task now is to conduct the negotiations ... in the best possible spirit, securing the least disruptive outcome," said Tusk, who warned last month that emotions stirred up on either side of the English Channel during the British election campaign were jeopardising agreement.
French Prime Minister Edouard Philippe was quick to scotch a suggestion Britain might do a U-turn and ask to stay in the bloc - something that would need EU agreement - and a Commission spokesman resisted a barrage of questions at a press briefing on whether the Union might agree to extend the two-year deadline.
Few Europeans voiced much sympathy for May. Some compared her to her predecessor David Cameron, who sought to silence Eurosceptic fellow Conservatives by calling the referendum on EU membership which ended his career and shocked Europe.
"YET ANOTHER OWN GOAL"
"Yet another own goal, after Cameron now May, will make already complex negotiations even more complicated," tweeted Guy Verhofstadt, the liberal former Belgian premier who is the European Parliament's point man for the Brexit process.
German conservative Markus Ferber, an EU lawmaker involved in discussions on access to EU markets for Britain's financial sector, was scathing: "At the most untimely point," he said, "The British political system is in total disarray. Instead of strong and stable leadership we witness chaos and uncertainty."
May, who had campaigned against Brexit last year, delivered her terms for withdrawal on March 29 that included a clean break from the EU single market. She then called a snap election hoping for a big majority to strengthen her negotiating hand.
That was also the broadly desired outcome in Brussels, where leaders believed that a stronger May would be better able to cut compromise deals with the EU and resist pressure from hardline pro-Brexit factions in her party to walk out without a deal.
European leaders have largely given up considering the possibility that Britain might change its mind and ask to stay, something May made clear was not her intention.
Most now appear to prefer that the bloc's second-biggest economy leave smoothly and quickly. Having recovered from last year's shock, Germany, France and other powers see Brexit as a chance to tighten EU integration without the awkward British.
As news of British mayhem broke, Juncker was launching a new push for an expanded EU defence project which Britain has long opposed, fearing a clash with the U.S.-led NATO alliance.
FEAR OF COLLAPSE
A breakdown in negotiations could mean Britain ceasing to be an EU member without having in place the legal agreements that would avoid a chaotic limbo for people and businesses. That would also make it improbable that Britain could secure the rapid free trade agreement it wants with the EU after it leaves.
In a note to clients, UBS wrote that a breakdown in talks was now more likely and would make it harder to reach a trade deal: "A tighter political balance could make it easier for Eurosceptics ... to prevent the government from offering the compromises needed to secure a trade deal."
Barnier aims to start with talks on residence rights for expatriates, on how much Britain will owe the Union on departure and on EU-UK border arrangements in Northern Ireland. He hopes outline agreements on those issues by the end of this year can open the way for discussion on a future trade deal. However, May and her allies have questioned the EU's negotiating proposals.
May's reappointment and determination to soldier on without a clear majority has muted talk of a different ruling coalition taking power with a mission to seek a "softer" Brexit than May is pursuing, possibly seeking to remain in the single market.
While the other 27 states would quite possibly be willing to extend to Britain the same kind of access to EU markets they offer to Norway or Switzerland, they have made clear that would mean Britain continuing to pay into the EU budget and obey EU rules, including on free migration across the bloc, while no longer having any say in how the Union's policies are set.
"Maybe there wont be a hard Brexit," Norwegian Foreign Minister Boerge Brende said. "Maybe Britain will have to show greater flexibility in the negotiations."
But EU officials question how any British government could persuade voters to accept a Norway-style package and so would be wary of starting down the path of negotiating it for fear of ending up without a deal that both sides could ratify in 2019. (Editing by Janet Lawrence)