* Brexit-backing ministers voice support
* May says still working with Northern Irish DUP
* Sterling up half a cent vs dollar (Adds comment from new Brexit Secretary Stephen Barclay)
By Costas Pitas and Alistair Smout
LONDON, Nov 16 (Reuters) - British Prime Minister Theresa May won the backing of the most prominent Brexiteer in her government on Friday as she fought to save a draft European Union divorce deal that has stirred up a plot to force her out of her job.
More than two years after the United Kingdom voted to leave the EU, it is still unclear how, on what terms or even if it will leave as planned on March 29, 2019.
Just hours after announcing that her senior ministers had collectively backed her divorce deal, May was thrust into her premiership's most perilous crisis when her Brexit Secretary Dominic Raab resigned on Thursday to oppose the agreement.
Other mutinous lawmakers in her party have openly spoken of ousting her and said the Brexit deal would not pass parliament.
But May, who has defiantly vowed to stay on as prime minister, got a rare boost on Friday when Michael Gove, the most prominent Brexit-supporting minister, gave his backing to her, saying he would stay on as environment minister.
Asked if he had confidence in May, Gove told reporters: "I absolutely do."
"I think it's absolutely vital that we focus on getting the right deal in the future, and making sure that in the areas that matter so much to the British people we can get a good outcome," said Gove, 51, a potential successor to May.
Trade minister Liam Fox, another leading Brexit supporter, joined Gove in backing May - but her future remains uncertain.
The first question she faced on an LBC radio phone-in show to defend her deal was from a caller who asked her to "respectfully stand down". She did not immediately address that part of the caller's question.
Stephen Barclay, a little-known junior health minister, was appointed as the new Brexit secretary, although the status of the role was downgraded from chief negotiator with May leading the completion of talks with the EU.
"We now need to keep up the momentum to finalise the Withdrawal Agreement and outline political declaration, and deliver a Brexit that works for the whole UK," Barclay tweeted.
May's spokesman said Barclay would have a domestic role. "The PM will be completing the last 10 days of negotiations," he said. Former interior minister Amber Rudd was named work and pensions secretary, replacing Esther McVey who also quit over the Brexit plan.
Sterling, which has see-sawed on Brexit news since the referendum, was up half a cent against the dollar at $1.2834 on Friday.
Politicians, officials and diplomats in London openly questioned how long May had left as speculation swirled that a leadership challenge could come soon.
Under Conservative Party rules, a vote must take place when 48 of her lawmakers submit letters to the party's so-called 1922 committee, chaired by a senior lawmaker, Graham Brady.
Influential Brexit-supporting lawmaker Steve Baker said rebels in May's party were close to that threshold. So far, at least 21 lawmakers have publicly said they have submitted letters, and others may have done so privately.
"I think we're probably not far off," said Baker, a key figure in the Brexit-backing wing of May's party. "I think it probably is imminent, yes," he told BBC TV.
British political correspondents reported that Gove, Fox and other pro-Brexit ministers would meet this weekend to amend May's deal. However, both the Irish and Dutch prime ministers said there was little scope to change the proposals.
Since she won the top job in the turmoil that followed the 2016 referendum, May's premiership has been characterised by obduracy in the face of frequent crises.
Her de facto deputy, David Lidington, said she would win a vote of no confidence, in which she would need a simple majority of votes cast by conservative lawmakers: "If those letters were to go in, I think that she would win any such vote decisively, and she'd deserve to do so."
If her divorce deal is voted down, the ultimate outcome of Brexit would be uncertain. Other possible scenarios include May's deal ultimately winning approval in a new parliamentary vote; May losing her job; Britain leaving the bloc with no agreement; or even another referendum.
A snap poll by Survation of 1,070 voters for the Daily Mail newspaper found 49 percent of respondents opposed the deal and just 27 percent backed it.
The deal is due to be discussed at an EU summit on Nov. 25.
By seeking to preserve the closest possible ties with the EU, May has upset her party's many advocates of a clean break, and Northern Ireland's Democratic Unionist Party (DUP), which props up her minority government.
"They've raised some questions with us, they've raised some concerns with us and yes we are looking at those," May said. "We are still working with the DUP."
The EU and Britain need an agreement to keep trade flowing between the world's biggest trading bloc and the United Kingdom, home to the biggest international financial centre.
May told LBC radio the threat of a no deal Brexit was personal as she is Type 1 diabetic: "I depend on insulin every day. My insulin is produced by a country elsewhere in the European Union."
May's spokeswoman said there had been strong business support for her draft deal.
But aero-engine maker Rolls-Royce's boss Warren East said his firm was pressing on with contingency plans, including "buffer stocks so that we have all the logistical capacity that we need to carry on running our business." (Additional reporting by Andrew MacAskill, Andy Bruce, Elizabeth Piper and William James; writing by Michael Holden and Guy Faulconbridge. Editing by Matthew Mpoke Bigg, William Maclean, Andrew Heavens and Peter Graff)