* Farage, face of opposition to EU, steps down as UKIP boss
* Two more Conservatives launch bids to become PM
* Andrea Leadsom gets backing of Boris Johnson to be PM
* Law firm starts action to demand Parliament say on Brexit
* Labour deputy leader to hold emergency talks with unions (Adds Johnson backing for Leadsom, Labour's Watson, StandardLife)
By Kylie MacLellan and Elizabeth Piper
LONDON, July 4 (Reuters) - The leader of the insurgentright-wing UK Independence Party said on Monday he was steppingdown after realising his ambition to win a vote for Britain toleave the EU, the latest twist in a dramatic reshaping of thenation's politics.
The departure of brash former commodities trader NigelFarage would sideline one of the most outspoken and effectiveanti-EU campaigners from the debate about how to sever Britain'sties with the other 27 countries in the bloc.
But it could also give his UKIP party - which underBritain's winner-takes-all election system won just one seat inParliament last year despite capturing 12.6 percent of the vote- an opportunity to select a less-polarising figure and take onthe mainstream in a radically altered political environment.
The June 23 'Brexit' vote to leave the EU has thrown the twomain political parties into disarray, with the rulingConservatives seeking a replacement for Prime Minister DavidCameron and lawmakers from the main opposition Labour Partyvoting to withdraw confidence in leader Jeremy Corbyn.
"I have never been, and I have never wanted to be, a careerpolitician. My aim in being in politics was to get Britain outof the European Union," said Farage, who remains a UKIP memberof the European Parliament.
"During the referendum campaign, I said 'I want my countryback'. What I'm saying today, is, 'I want my life back,' and itbegins right now."
With Labour's Corbyn so far refusing to step down andissuing a video appealing for unity, fellow lawmaker AngelaEagle said she had the necessary support to trigger a leadershipchallenge and resolve the "impasse" crippling the party.
Deputy leader Tom Watson plans emergency talks with tradeunion representatives, Labour's financial backers, on Tuesday ina "last throw of the dice" to try and reach a deal over Corbyn'sfuture.
The acrimonious leadership battles in the main politicalparties have added to uncertainty at a time when Britain isembarking on its biggest constitutional change since thedissolution of its empire in the decades after World War Two.
Global markets have been hit by uncertainty over the impactof Brexit on trade and investment, and concerns that Britain'sdeparture could prompt other EU members to consider followingsuit.
George Osborne, the finance minister, has abandoned histarget of balancing the budget within four years and on Sundayfloated the idea of a quick cut in the rate of corporation taxto less than 15 percent from 20 percent to show that Britain wasstill "open for business". Labour accused him of trying to turnthe country into an offshore tax haven.
Osborne told Parliament he would meet the heads of majorbanks on Tuesday for discussions on Brexit.
"We are not today - although we remain vigilant - talkingabout a banking crisis, despite a very significant adjustment infinancial markets," he said.
Standard Life suspended dealing in its UK Real Estatefund following a rapid increase in redemption requests in thewake of the Brexit vote. Analysts said other funds could takesimilar action.
The pound has recovered only slightly from a 31-year low,and the FTSE 100 share index fell 0.8 percent on Monday,although it has gained 3 percent since the referendum.
A WOMAN PM?
Theresa May, a Conservative party stalwart who has run thelaw-and-order portfolio in the cabinet for six years, is thefavourite to succeed Cameron despite having campaigned to remainin the EU.
According to bookmakers, her strongest rival is AndreaLeadsom, 53, a junior minister who was unknown to most Britonsbefore the referendum campaign but was widely judged to havemounted an effective case for 'Leave' in an eve-of-votetelevised debate seen by millions.
If the betting odds are correct, Britain is on course to getits first woman prime minister since Margaret Thatcher leftoffice in 1990.
Leadsom set out her leadership credentials on Monday and gotthe backing of former London Mayor Boris Johnson.
She said talks over Britain's departure from the EU shouldbe as short as possible to avoid prolonged uncertainty.
She offered reassurance to EU nationals currently living inBritain: "I commit today to guaranteeing the rights of our EUfriends who've already come here to live and work. We must givethem certainty."
But immigration minister James Brokenshire said the UnitedKingdom should make no such guarantee unless it receivedreciprocal assurances about the rights of expatriate Britons.
DIVORCE PROCESS
Despite the 52 percent referendum vote, Britain has not yetinvoked Article 50 of the EU's Lisbon Treaty to begin the formalprocess of breaking away. While all the candidates to succeedCameron say there is no going back, some anti-Brexit politicianssay it is not a foregone conclusion.
Law firm Mishcon de Reya said on Monday it had started legalaction to demand the government win approval from Parliamentbefore triggering the divorce process. Most of the 650 membersof the House of Commons opposed Brexit before the vote.
"The outcome of the Referendum itself is not legally bindingand for the current or future Prime Minister to invoke Article50 without the approval of Parliament is unlawful," KasraNouroozi, a partner at Mishcon de Reya, said in a statement.
Former defence minister Liam Fox, a pro-Brexit figure and anoutsider in the leadership contest, said Britain should activateArticle 50 before the end of the year, and he did not believeany parliamentary vote was needed.
He said the free movement of people across Europe - a coreprinciple of the EU but a major concern for many Britons -should not be on the table in negotiations about a trade dealwith the EU after Brexit.
The other leadership contenders are work and pensionsminister Stephen Crabb and justice minister Michael Gove, aLeave campaigner who caused high political drama last week byturning against his ally, Johnson, and driving him from therace. (Additional reporting by Alistair Smout, Paul Sandle, MichaelHolden, Sarah Young, William James, Andy Bruce, WilliamSchomberg and James Davey; Writing by Mark Trevelyan; editing byAnna Willard and Dan Grebler)
