* Race to replace May as party leader officially begins
* Boris Johnson promises tax cuts for higher earners
* Foreign minister Hunt says he's the serious candidate
* Raab: "I'm the Brexiteer you can rely on"
* Hancock: "We need leader, not leaver or remainer" (Updates after campaign launches)
By William James and Elizabeth Piper
LONDON, June 10 (Reuters) - Leading Brexit advocate Boris Johnson promised tax cuts for higher earners if he becomes Britain's next prime minister as the contest to replace Theresa May - and take charge of the EU divorce - officially kicked off on Monday.
May stepped down as leader of the ruling Conservative Party on Friday, having failed three times to win parliament's support for a European Union divorce deal that was supposed to address Britain's biggest political crisis in a generation.
Nominations to replace her must be submitted on Monday, and each of the 11 declared candidates needs to secure at least eight backers from the Conservatives' 300-plus elected lawmakers.
A number of the contenders look set to fall short, and voting later this week will whittle the field down further.
At campaign launches on Monday, several made their pitches. While all were keen to set out a domestic agenda, it was Brexit that dominated.
Nearly all promised that they could solve the Brexit conundrum - which eluded May in three years of EU talks - in just three months, between the new leader being chosen at the end of July and the current exit date of Oct. 31.
"Without Brexit, there will be no Conservative government and maybe no Conservative party," foreign minister Jeremy Hunt said at his campaign launch. "From my conversations with European leaders, it is clear to me there is a deal to be done; they want us to come up with proposals."
"THE BREXITEER YOU CAN RELY ON"
Dominic Raab, who quit as Brexit minister over May's divorce deal, said he too could get a new agreement but promised that the United Kingdom would leave the EU on Oct. 31, even if that meant reverting to basic World Trade Organization trade terms.
"I'm the Brexiteer that you can rely on," he said.
At his launch, health minister Matt Hancock, who has ruled out a no-deal departure, said: "We don't need a 'leaver', we don't need a 'remainer', we need a leader for the future."
The differences between the candidates reflect the Conservative disunity on the issue, which has meant that, three years after the United Kingdom voted by 52% to 48% to quit the EU, it remains unclear how, when or even whether it will leave.