(Repeats story sent on Thursday, no changes to text)
* May says Brexit vote is demand for "fairer" society
* Keynote speech signals radical break with predecessors
* May says government is a force for good
* Sterling falls to 31-year low
By Guy Faulconbridge
LONDON, Oct 6 (Reuters) - For Prime Minister Theresa May, Britain's vote to leave the European Union is a demand for the biggest change in at least a generation in the way the United Kingdom is run.
This week May cast the Brexit vote as a "quiet revolution" that exposes the failings of modern Britain in a way that can no longer be ignored by a leader who looks to Margaret Thatcher, Winston Churchill and Clement Attlee for inspiration.
The prime minister promised fundamental - though yet to be detailed - reforms to fix problems ranging from arrogant elites and venal bosses to workers' rights, immigration and Britain's obsession with privilege.
"This is a turning point for our country. A once-in-a-generation chance to change the direction of our nation for good," May told members of her ruling Conservative Party.
"Change has got to come too because of the quiet revolution that took place in our country just three months ago - a revolution in which millions of our fellow citizens stood up and said they were not prepared to be ignored anymore," she said.
May, who said the poor had made the biggest sacrifices since the 2008 global financial crisis, said Britain needed selective schools to help talented poor students, a new industrial strategy, workers on company boards and more house building.
The 60-year-old former interior minister won the top job in the turmoil which followed the June 23 Brexit vote, despite having been a low-key supporter of the 'remain' camp.
May is an unlikely radical, but her words indicate she plans some of the biggest changes to British society since Thatcher's 1979-1990 premiership, even as she embarks on one of the most complex negotiations in recent European history: Britain's EU exit.
To be sure, May was speaking to her own party faithful while staking her claim to the so-called 'centre ground' of British politics by pocketing policies and rhetoric from rivals such as Labour and the United Kingdom Independence Party.
May, a vicar's daughter, was also seeking to unite a country whose divisions were laid bare by the referendum, in which England and Wales voted to leave the EU while Scotland and Northern Ireland backed remain. Scotland has said the outcome could prompt a second Scottish independence referendum.
In her speech, as is customary for a Conservative leader, May praised free markets, free trade and the father of modern conservatism, 18th century British politician Edmund Burke.
But she also sketched out new ideas that would, if successful, undo 30 years of British political thinking by putting the state firmly back in the hot seat as the initiator and arbiter of change.
"Government can and should be a force for good," she said, using language more associated with the opposition Labour Party. "We should employ the power of government for the good of the people."
"The state exists to provide what individual people, communities and markets cannot," May said, invoking Attlee's post-war reforming Labour administration and adding that she would use social reform to build "a society based on fairness".
That is a sharply different vision of Britain to that set out by almost all of her predecessors since Thatcher, who once declared there is "no such thing as society".
May even had some advice for Mark Carney, the governor of the Bank of England, on the pain of low interest rates and quantitative easing.
The Sun newspaper said in an editorial that May's aim was "to reboot Britain" and praised her for huge ambition but cautioned that she should not build a more expensive state.
But many in Britain will be sceptical about May's ability, especially given her small parliamentary majority, to deliver on her promises and Labour lawmaker John Mann said she lacked a mandate to do so, having yet to win an election as prime minister.
"She is overstating her position by claiming Brexit gives her a mandate for all this change," he said. "She does not have a mandate - she is chronically lacking one."
The clearest reality check for May's ambitions this week came from the currency markets, where sterling has fallen more than 3-1/2 cents to a 31-year low against the dollar since her announcement on Sunday that she would trigger the formal EU divorce process by the end of March.
Her rhetoric spooked investors who have started to bet that Britain is facing a "hard Brexit", meaning it will give up trying to remain in the EU's single market in order to impose controls on immigration from the other 27 EU member states.
May dismissed talk of a "hard Brexit" but in private meetings some government ministers have indicated at least one significant break with the approach of her predecessor David Cameron: its view of the City, London's financial powerhouse.
While May said that financial services were one of many strategic sectors, two financiers who declined to be identified said it had been made clear to them by a government minister that their concerns over being able to sell into EU markets after Brexit were overblown.
"I don't know how they are going to extract us from the European Union and to remake society as well," said one financier who attended one of the meetings.
"Welcome to hard Brexit and you know what - I am scared this is going to cost a hell of a lot."
Reporting by Guy Faulconbridge; Editing by Gareth Jones