By Estelle Shirbon and Paul Sandle

LONDON (Reuters) - Two leading contenders to be the next British prime minister disagreed publicly on Sunday on how quickly negotiations should be triggered to plan a departure from the European Union.

Interior minister Theresa May, the front-runner who campaigned for a "Remain" vote in the June 23 referendum, said Britain needed to have a clear negotiating position and she would not be rushed into starting the formal exit process this year.

Junior energy minister Andrea Leadsom, who has emerged as a strong rival to May from the "Leave" camp, struck a more urgent note, saying Britain had to "get a grip and make progress".

Britons voted by 52 to 48 percent to leave the bloc it had joined in 1973, defeating a campaign led by Prime Minister David Cameron, who announced his resignation the following morning.

Adding to the political turbulence, the vast majority of the main center-left opposition Labour Party's lawmakers openly denounced their leader Jeremy Corbyn as unfit for the job but he has refused to resign, citing grassroots support.

Five candidates are vying to succeed Cameron as Conservative Party leader and prime minister. The field will be whittled down to two by the party's lawmakers over the summer, before party members pick the winner by Sept. 9.

"NO CORONATION"

May has established an early lead, gaining the support of more than 100 lawmakers, reports said on Sunday, four times as many as any other candidate.

But her critics, including rivals Leadsom and Justice Secretary Michael Gove, said the next leader needed to come from the winning "Leave" side of the EU debate.

May, who vowed to honor the vote when she launched her bid on Thursday, said Britain needed a leader who could bring the country back together.

"(People) are not looking for a prime minister who is just a Brexit prime minister, but a prime minister who can govern for the whole of the country," she said in an interview on ITV.

The shock decision to leave the EU has pushed the pound to 30-year lows and raised concerns that the British economy could go into reverse.

Media reports on Sunday suggested that some Conservative lawmakers wanted Leadsom and other candidates to stand aside so that May could be installed quickly in Downing Street to establish stability and start making progress towards Brexit.

But May said she did not favor the "coronation" scenario". "I think there should be a contest," she said.

"GET A GRIP"

EU leaders have been putting pressure on Britain to trigger article 50 quickly to set the exit process in motion and avoid a prolonged period of uncertainty that is also destabilizing for the other 27 member states.

Once the article is invoked, the clock starts ticking for an exit deal to be agreed within two years.

"We've got to be clear about what our negotiating stance is before we trigger that article 50, because once we trigger it then all the processes start," said May.

But former banker Leadsom, who was one of the most passionate advocates of Brexit during the referendum campaign, said she would move as quickly as possible.

"It's about giving certainty to businesses, it's about saying to the world 'we're open for business'," she told BBC TV.

"We need to get on with it, we need to get a grip and make progress."

Leadsom, who is not well known to many Britons, is eclipsing her senior colleague Gove, whose own campaign is struggling to escape the charges of betrayal towards leading "Leave" campaigner Boris Johnson.

Gove withdrew his support for former London mayor Johnson and decided to run against his former ally on Thursday.

The final choice of leader, and Britain's next prime minister, will come down to a vote of about 150,000 members of the Conservative Party.

A poll of Conservative voters in the Mail on Sunday newspaper gave May overwhelming 86 percent support in a head-to-head against Leadsom.

(Additional reporting by Michael Holden; Editing by Keith Weir)