By Michael Holden and Elizabeth Piper
LONDON (Reuters) - British Prime Minister Theresa May won support from many of her ministers, including a leading eurosceptic, on Tuesday after two top cabinet members quit saying her Brexit plan was too half-hearted.
May said she had chaired a "productive" meeting of her government, unswayed by the resignations on Sunday and Monday of Foreign Secretary Boris Johnson - the face of Brexit for many Britons - and Brexit negotiator David Davis.
U.S. President Donald Trump acknowledged that his visit to Britain from Thursday came at a time of "turmoil".
Among those rallying around May was environment minister Michael Gove - a prominent campaigner to exit the European Union alongside Johnson before the 2016 referendum - who said he would not resign.
With less than nine months left until Britain is due to leave the bloc, May is sticking to her plan for a "business friendly" Brexit.
She looks set on facing down hardline Brexit supporters in her Conservative Party who are livid over her plans to negotiate a "free trade area for goods" with the EU. One described accepting EU rules as "the ultimate betrayal".
Above a picture of her cabinet, including her new foreign secretary, Jeremy Hunt, and Brexit minister Dominic Raab, May tweeted: "Productive Cabinet meeting this morning - looking ahead to a busy week."
Her spokesman said the cabinet had discussed the publication of a "white paper" policy document on Britain's future ties with the EU and stepping up preparations for any no-deal outcome to the negotiations with Brussels.
"ONE VOICE"
"I think it is right that the cabinet backs the prime minister and speaks with one voice - and if people don't do that then they have to go," Justice Secretary David Gauke told BBC radio.
May must now quickly seek EU support for her Brexit proposal. Talks have all but stalled because of her reluctance to show her cards until now for fear of angering one of the two main factions of her party.
German Chancellor Angela Merkel arrived in London for a meeting with May and other leaders to discuss the Western Balkans. She was expected to give a news conference alongside May.
Trump, answering a reporter's question about whether May would stay in power, said: "That's up to the people. I get along with her very well, I have a very good relationship."
In response to those comments, May's spokesman said that she "looks forward to showing Donald Trump the UK and talking to Donald Trump about the UK and is confident that he will leave the UK with a positive view".
The British leader may have quelled talk of a leadership challenge, but some Conservative Brexit supporters are still incensed over what they see as her breach of a promise of a clean break with the EU.
"It is the ultimate betrayal of our democracy and people's belief in it. It's not even an accidental betrayal, it was planned and plotted well in advance," said Conservative lawmaker Andrew Bridgen.
"Never have so many campaigned for so long and so hard for so little," he told Reuters.
"SEMI-BREXIT"
Many Brexit campaigners still hope for a vote of confidence to oust May, but it is unlikely that they have the numbers. They also lack the support in parliament to try to change any deal that is agreed with the EU.
Meeting Conservative lawmakers on Monday, May was cheered and applauded by many, having warned that squabbling could pave the way for socialist opposition leader Jeremy Corbyn to take power.
May's proposals for a future EU relationship after Britain departs from the bloc next March had taken two years of internal government wrangling to agree. But within 48 hours Davis had quit, saying she had already given too much away to the EU, and Johnson followed.
"Brexit should be about opportunity and hope," Johnson said in a scathing resignation letter that was echoed in headlines in a number of national newspapers. "That dream is dying, suffocated by needless self-doubt." He said Britain was heading for a "semi-Brexit".
The Sun, Britain's biggest-selling newspaper, which has long argued for Brexit, said May had made "blunder after blunder".
"Now there is chaos," it said in its editorial. "Brussels must not mistakenly conclude, as EU Council chief Donald Tusk hinted, that one more push will destroy Brexit. Brexit must and will happen."
But others argued that May had adopted the most realistic plan after losing her parliamentary majority in an ill-judged election last year, leaving her reliant on a small Northern Irish party to govern.
"If people don’t like this proposal, what is their alternative?" Gauke asked. "The challenge is (that it is) all very well for people to say 'I wouldn't do this'. But remember, what are the options in front of us?"