* Conservative Party's agenda overshadowed by Brexit
* Party's rating down 6 points to 29 percent in new poll
* Britons await next move in Brexit stalemate
By William James
LONDON, April 14 (Reuters) - Britain's ruling Conservative Party cannot let itself be defined solely by Brexit, Prime Minister Theresa May's de facto deputy said on Sunday, as polling showed failure to leave the European Union on schedule has badly damaged its support.
May's authority has been shattered by her three-time failure to get an exit deal approved by parliament and a pledge to quit once Brexit is delivered, driving speculation about her successor and a possible national election.
The once-prized stability of British politics has disappeared, threatening to break apart both the Conservatives and their main opponents Labour, and leaving the world's fifth-largest economy facing an uncertain future.
Without any consensus in parliament, reflective of a deeply divided population, all outcomes remain possible in the coming weeks and months: leaving the EU with a deal, a disorderly exit without a deal, or another vote on whether to leave at all.
"We mustn't define ourselves as the Brexit party," said David Lidington, cabinet office minister and effectively May's second in command.
"We've got to deliver the outcome of the referendum ... but, the Conservative Party has got to remain a broad church, a national party, and it's got to be talking about things that matter to people in their everyday lives: housing, health service, living standards."
May, 62, took power in the aftermath of Britain's surprise 2016 vote to leave the EU and has seen her government paralysed by divisions over Brexit and unable to enact an ambitious reform agenda to tackle social injustice.
An Opinium poll published in the Observer newspaper showed the Conservatives at 29 percent, down 6 points from March 28 and 7 points behind Labour.
An analysis of polls since the original intended March 29 exit day, published in the Sunday Telegraph, showed the Conservatives would lose 59 parliamentary seats if an election were held.
"Much of this drop reflects disappointment among Leave voters - around a half of whom would prefer 'no deal' - at the government's failure to deliver Brexit," polling expert John Curtice wrote in the Sunday Telegraph
The analysis showed Corbyn's Labour Party would win the most seats but still fall short of an outright majority in the 650-seat parliament, with Scottish nationalists and the small centrist Liberal Democrats party also picking up seats.
"KICKED THE CAN"