* EU blocks May's attempt to move talks on
* Weakened leader faces party infighting
* May moves to reassure business
* EU leaders might offer May a hand (Adds further May, source on business meeting)
By Elizabeth Piper and Alastair Macdonald
LONDON/BRUSSELS, Oct 9 (Reuters) - Britain and its European Union partners clashed on Monday over which side should make the next move to unblock Brexit talks, despite concerns they will miss a deadline for a divorce deal and that London is heading for a chaotic departure.
Prime Minister Theresa May made clear in a speech she delivered to parliament that she hoped her EU partners would make proposals at a new round of talks opening the way to the next stage of negotiations, saying "the ball is in their court".
But even before she had delivered her address, an EU spokesman hit back in Brussels, saying "the ball is entirely in the UK court for the rest to happen".
May is desperate to try to regain some of her authority and refocus on talks to unravel 40 years of union after a speech at her party conference last week, marred by a repetitive cough, a prankster and a stage malfunction, left her weaker than ever.
She has so far fought off attempts to unseat her by critics already angry over an ill-judged election when she lost her governing Conservatives' majority. But her weakness has opened the door for many in the party to challenge her Brexit strategy with just 18 months to go before Britain leaves the EU.
With Brussels quietly preparing for a collapse in the talks and Britain getting ready for what May calls "every eventuality", some officials and business chiefs worry the country will crash out of the EU without a deal.
Speaking in parliament, May said her negotiators had made progress on the first phase of talks, tackling the rights of expatriates and the border with EU-member Ireland, and that she was determined to secure a new partnership with the other 27 members of the wealthy political and trade bloc.
"Achieving that partnership will require leadership and flexibility, not just from us but from our friends, the 27 nations of the EU," she told a raucous session of parliament.
"And as we look forward to the next stage, the ball is in their court. But I am optimistic we will receive a positive response."
But the EU stuck to its terms: "There is a clear sequencing to these talks and there has been so far no solution found on step one, which is the divorce proceedings," European Commission spokesman Margaritis Schinas told a regular briefing. "So the ball is entirely in the UK court for the rest to happen."
May, who hosted businesses on Monday to listen to their Brexit concerns, is keen to push the talks beyond a discussion of the divorce to try to offer firms some certainty about future trading conditions.
According to a source familiar with the matter, May told business leaders that for her, a roughly two-year transitional agreement was non-negotiable. "It will happen," the source said when asked what May had spoken about.
She also said her government had no intention of revoking Article 50, which triggered the Brexit talks in March this year, and stopping Britain's departure.
But a lack of progress in talks some 15 months after Britain voted to leave the EU in a referendum has added pressure on May, who was criticised by the opposition for failing to offer any clarity on what the future relationship will look like.
"Now the reality for this Tory (Conservative) government is beginning to bite, but if things do not improve, the reality may soon begin to bite for the jobs and living standards of the people of this country," said Jeremy Corbyn, leader of the opposition Labour Party.
A report that aerospace manufacturer BAE Systems is planning to cut more than 1,000 jobs did little to ease those concerns that without progress in the talks, firms will start to make staffing and relocation decisions.
EU negotiators say that while they see no big breakthrough at the summit next week, they may offer May a hand by offering hope of a shift at the next scheduled meeting in mid-December.
Aides to May have signalled that the prime minister has accepted that her October deadline will not be met despite a speech in Italy last month which attempted to reset the tone of the difficult negotiations.
But some pro-Brexit campaigners are calling on the prime minister to get ready to step away from the talks - underlining the deep divisions in the Conservative Party.
Those differences were aired again on Monday with negative briefings in the local media against finance minister Philip Hammond, who supports prolonging the status quo with the EU for as long as possible, and foreign minister Boris Johnson, who angered some Conservatives for setting his own Brexit red lines.
Some have suggested that May will reshuffle her cabinet, but her spokesman said she had full confidence in both ministers.
"We are fast reaching the point when the prime minister should assert the authority of her office over the negotiations and call time," Bernard Jenkin, a Conservative lawmaker, wrote in the Guardian newspaper.
John Baron, another pro-Brexit campaigner, called on the government to "prepare more thoroughly for a 'no deal'".
"I have long believed that the EU Commission primarily wants to punish Britain for daring to leave the organisation," he said. "We should have no fears about a 'no deal' scenario." (Additional reporting by Lily Cusack in Brussels and William James in London; Editing by Peter Graff/Mark Heinrich)